# Quantum communication networks with defects in silicon carbide

Sebastian Ecker<EMAIL_ADDRESS>Quantum Technology Laboratories
GmbH (qtlabs), Clemens-Holzmeister-Straße 6/6, 1100 Vienna, Austria  Matthias
Fink  Quantum Technology Laboratories GmbH (qtlabs), Clemens-Holzmeister-
Straße 6/6, 1100 Vienna, Austria  Thomas Scheidl  Quantum Technology
Laboratories GmbH (qtlabs), Clemens-Holzmeister-Straße 6/6, 1100 Vienna,
Austria  Philipp Sohr  Quantum Technology Laboratories GmbH (qtlabs), Clemens-
Holzmeister-Straße 6/6, 1100 Vienna, Austria  University of Vienna, Faculty of
Physics & Vienna Doctoral School in Physics, Boltzmanngasse 5, A-1090 Vienna,
Austria  Atominstitut, Technische Universität Wien, 1020 Vienna, Austria
Rupert Ursin  Quantum Technology Laboratories GmbH (qtlabs), Clemens-
Holzmeister-Straße 6/6, 1100 Vienna, Austria  Muhammad Junaid Arshad
Institute of Photonics and Quantum Sciences, SUPA, Heriot-Watt University,
Edinburgh EH14 4AS, United Kingdom  Cristian Bonato  Institute of Photonics
and Quantum Sciences, SUPA, Heriot-Watt University, Edinburgh EH14 4AS, United
Kingdom  Pasquale Cilibrizzi  Institute of Photonics and Quantum Sciences,
SUPA, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom  Adam Gali
HUN-REN Wigner Research Centre for Physics, PO. Box 49, H-1525 Budapest,
Hungary  Department of Atomic Physics, Institute of Physics, Budapest
University of Technology and Economics, Műegyetem rakpart 3., H-1111 Budapest,
Hungary  MTA-WFK Lendület "Momentum" Semiconductor Nanostructures Research
Group, PO. Box 49, H-1525 Budapest, Hungary  Péter Udvarhelyi  HUN-REN Wigner
Research Centre for Physics, PO. Box 49, H-1525 Budapest, Hungary  Department
of Atomic Physics, Institute of Physics, Budapest University of Technology and
Economics, Műegyetem rakpart 3., H-1111 Budapest, Hungary  Alberto Politi
Oliver J. Trojak  School of Physics and Astronomy, University of Southampton,
Southampton SO17 1BJ, United Kingdom  Misagh Ghezellou  Jawad Ul Hassan  Ivan
G. Ivanov  Nguyen Tien Son  University, Department of Physics, Chemistry and
Biology, SE-58183 Linköping, Sweden  Guido Burkard  Benedikt Tissot
Department of Physics, University of Konstanz, D-78457 Konstanz, Germany  Joop
Hendriks  Carmem M. Gilardoni  Caspar H. van der Wal  Zernike Institute for
Advanced Materials, University of Groningen, NL-9747AG Groningen, The
Netherlands  Christian David  Paul Scherrer Institut, CH-5232 Villigen,
Switzerland  Thomas Astner  Institute for Quantum Optics and Quantum
Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090
Vienna, Austria  Philipp Koller  Institute for Quantum Optics and Quantum
Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090
Vienna, Austria  University of Vienna, Faculty of Physics & Vienna Doctoral
School in Physics, Boltzmanngasse 5, A-1090 Vienna, Austria  Michael Trupke
<EMAIL_ADDRESS>Institute for Quantum Optics and Quantum Information
(IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria

###### Abstract

Quantum communication promises unprecedented communication capabilities
enabled by the transmission of quantum states of light. However, current
implementations face severe limitations in communication distance due to
photon loss. Silicon carbide (SiC) defects have emerged as a promising quantum
device platform, offering strong optical transitions, long spin coherence
lifetimes and the opportunity for integration with semiconductor devices. Some
defects with optical transitions in the telecom range have been identified,
allowing to interface with fiber networks without the need for wavelength
conversion. These unique properties make SiC an attractive platform for the
implementation of quantum nodes for quantum communication networks. We provide
an overview of the most prominent defects in SiC and their implementation in
spin-photon interfaces. Furthermore, we model a memory-enhanced quantum
communication protocol in order to extract the parameters required to surpass
a direct point-to-point link performance. Based on these insights, we
summarize the key steps required towards the deployment of SiC devices in
large-scale quantum communication networks.

##  I Introduction

The advent of the information age is not driven by computers alone, but
increasingly by the connection of many computers into ever-growing computer
networks. Similarly, quantum technologies will reveal their full potential
only by harnessing connections between distant quantum processors [1]. While
linking quantum processors will prove essential in quantum computing and
distributed quantum sensing [2], an intermediate goal is the exploitation of
quantum properties in the communication process itself.

The exchange of photons in quantum communication enables communication
primitives unachievable in the classical realm. In quantum cryptography, for
example, quantum states of light are used to exchange cryptographic keys which
are inaccessible by a third party by virtue of the no-cloning theorem [3, 4].
The main roadblock towards widespread deployment of quantum cryptography is
the limited communication distance of a few 100 km in optical fiber due to the
nonexistence of a quantum amplifier. Currently, there are two approaches of
extending the transmission distance of flying qubits. The first one involves
free-space links between optical ground receivers and satellites, an approach
which has seen the first in-field demonstrations in recent years [5].
Satellite-based quantum communication enables exchange of cryptographic keys
around the globe [6, 7], where the loss is dominated by diffraction instead of
absorption. The second approach relies on intermediate nodes in fiber-based
networks, which promise to overcome the fundamental limit of point-to-point
connections [8]. These nodes interface flying qubits with stationary qubits.
Not only do stationary qubits act as quantum memories to extend the
transmission distance of quantum states, but they also facilitate processing
and routing of quantum information in complex network topologies.

Quantum nodes should therefore simultaneously fulfill several requirements.
First and foremost, the transfer of quantum information to and from the nodes
should be faithful and efficient [9]. Secondly, the storage time, which is
limited by decoherence effects of the underlying physical system is crucial.
In particular, it should be long enough to enable local quantum processing in
addition to quantum and classical communication, both of which are limited by
the travel time of the photons over global distances and the success
probability of photon transmission. Ideally, the state can be transferred from
the spin memory to a long-lived quantum register which has orders of magnitude
longer storage times [10]. Crucially, the memories should emit in one of the
telecommunication wavelength bands in order to minimize transmission losses
and guarantee compatibility with existing fiber infrastructure. While quantum
frequency conversion is a viable solution for shifting frequencies to the
telecommunication band [11, 12, 13], noise and loss are inevitably added in
the process. In addition, the nodes should be hosted on a scalable and
integrated platform for parallelization and multiplexing purposes.

While several candidate systems such as atomic ensembles [14], quantum dots
[15, 16], rare-earth-doped solids [17, 18] and trapped ions [19] are currently
investigated, a particularly promising platform are defects in semiconductor
materials. Among those, a number of defects in silicon carbide have gained
attention due to their strong optical transitions, long spin coherence
lifetimes and the fact that they are hosted on a standard material in the
semiconductor industry [20]. The latter allows for a high level of
integration, electrical spin read-out, electrically driven single photon
emission and tunability via microcavity integration [21]. Additionally, spin
centers can be interfaced with time-bin qubits as well as polarization qubits
[22], making them versatile and deployable both for free-space and fiber-
optical quantum communication.

A central concept in the deployment of semiconductor defects for quantum
networks is spin-photon entanglement. These hybrid entangled states between a
stationary and a flying qubit facilitate heralded entanglement between two
quantum memories via Bell state measurements (BSM). To this end, two photons
are interfered on a beamsplitter in a synchronous BSM, or a single defect is
read out after two consecutive writing processes, which constitutes an
asynchronous BSM [23]. BSMs are also key in entanglement swapping, which in
turn is an essential building block of the quantum repeater protocol [8].
While first laboratory experiments have demonstrated heralded entanglement
distribution between quantum memories and basic quantum network operations
[17, 18, 24, 25], full-fledged quantum repeater chains which outperform point-
to-point connections in quantum cryptography are still a long way off.
However, several quantum cryptography protocols exhibit a substantial benefit
over the direct transmission of photons with only a single intermediate
network node. One of these protocols is memory-assisted quantum key
distribution (MA-QKD) [26], which is regarded an important milestone on the
path to outperforming direct transmission [27].

In this white paper we present the results of MA-QKD simulations with
parameters from state-of-the-art SiC devices. This serves as a testbed for the
performance of SiC memories in a relevant quantum communication setting.
Crucially, the results of this study provide the basis for the development of
a roadmap for SiC devices. Furthermore, we discuss advanced quantum
communication scenarios which benefit from the SiC platform. This paper is
organized as follows. In Sec. II.1 we introduce the silicon carbide platform
and the defects which are of interest, while Sec. II.2 is devoted to the
photonic properties of the defects and their integration in quantum devices.
Further on, we describe how these quantum devices based on SiC are suited as
quantum nodes in Sec. III.1. After a short introduction to quantum
cryptography, Sec. III.2 is dedicated to a particular memory-assisted QKD
protocol, with secure key rate simulation results presented in Sec. III.3. We
draw a roadmap for necessary improvements of SiC devices for quantum link
deployment in Sec. IV and summarize our white paper in Sec. V.

##  II The silicon carbide platform

###  II.1 Implementing spin-photon interfaces with defects in SiC

Single electron spins may be optically accessed through point defects in
semiconductors, such as SiC [28]. The electron spin of the isolated
paramagnetic defects in SiC can serve as a solid-state qubit once it can be
initialized, read out and coherently controlled [29, 30, 31, 32, 33, 34, 35].
Furthermore, nuclear spins of the host crystal proximate to the point defects,
e.g., 13C and 29Si in SiC, or introduced by the defect itself, e.g., 14N or
15N in nitrogen-vacancy defects [36, 37, 38, 33, 39, 40, 41, 42, 43] or 51V in
substitutional vanadium defects [44, 45, 46], can be used as quantum registers
or ancilla qubits mediated by the hyperfine interaction between them (e.g.,
Refs. 47, 48, 49). The quantum states of the electron spin and nuclear spins
can be typically controlled by microwave and radiofrequency alternating
magnetic fields, if necessary, in the presence of a constant magnetic field.

A coherent spin-photon interface (SPI) can be created by exploiting spin-
dependent atomic-like optical transitions [50, 32, 51, 35], typically
available at cryogenic temperature. Spin-selective optical transitions,
possibly in combination with microwaves for higher-spin systems [51], enable
the preparation of specific spin states by optical pumping. They also enable
readout by detection of the emitted photons under optical excitation [50], or
by conversion of spin-states into different charge states [52, 53, 54].
Coherent SPI’s also enable establishing a connection between the quantum
memory of the solid-state qubit and the flying qubit encoded into the chosen
quantum property of the photon [32]. This can be harnessed to setup
entanglement-based quantum communication. Very recently, the first
demonstration of spin-photon entanglement with a SiC defect was reported using
the silicon vacancy in 4H-SiC [55].

Architectures based on single point defects in materials with a diluted
nuclear spin bath have also shown the promising opportunity to coherently
control a register of nearby weakly-coupled nuclear spins [56]. In this case,
the hyperfine interaction acts on timescales longer than the electron spin
dephasing time, so that it does not result in a separate transition visible in
the electron spin resonance spectrum and cannot be driven directly. However,
researchers have been able to address and coherently control such nuclear
spins by applying pulse sequences such as dynamical decoupling on the electron
spin, that extend its coherence time and can effectively isolate the
contribution of a single weakly-coupled nuclear spin, filtering out all the
other background. These techniques have enabled the implementation of multi-
qubit schemes [57], such as quantum error correction [58]. While most of this
work has been done in diamond, some recent results show that it is also
possible in SiC [49]. Given the higher abundance of isotopes with non-zero
nuclear spin in SiC, however, isotopic engineering may be required to maximise
the number of controllable nuclear spins [59].

We note that the reduction of the density of 13C and 29Si nuclear spins can be
advantageous to extend the coherence times and reduce the optical linewidth of
the coherent emission [49, 35] which occurs at the no-phonon or zero-phonon-
line emission of the defects. It is imperative to fully characterize the
magneto-optical properties of these point defects, in order to develop
efficient quantum optics protocols for quantum information processing
applications such as quantum communication.

The most mature polytype of SiC is 4H-SiC which has about 3.3 eV band gap. To
realize a spin-to-photon interface, deep levels should be introduced by the
point defect. This can typically be achieved by introducing dangling bonds of
vacancies or dopants with $d$ and $f$ orbitals. We illustrate this by
comparing three types of deep-level point defects in SiC: the silicon-vacancy
(Si-vacancy), divacancy and vanadium centres in 4H-SiC (see Fig. 1). These
defects introduce multiple levels into the band gap where the excited state
can be described by promoting an electron from the occupied in-gap level to
the unfilled in-gap level. These defects have complementary ground state spin
structure, with the the negatively charged Si-vacancy having spin $S=3/2$ in
an orbital singlet, the neutral divacancy spin $S=1$, and the neutral vanadium
substituting silicon has spin $S=1/2$ in an orbital doublet.

Figure 1: (a) 4H-SiC crystal lattice with its stacking sequence, (b) Silicon-
vacancy and its electronic structure in the negative charge state at the
quasicubic site, (c) the neutral divacancy with a neighboring Si and C vacancy
with its electronic structure and (d), Vanadium substituting Si and its
electronic structure in the neutral charge state at the quasicubic site.

The electron-orbital and spin level structures are depicted for the three
selected qubit species (see Fig. 1). For the negatively charged Si-vacancy in
4H-SiC, in-gap localized defect states are generated by the four carbon
dangling bonds of the defect which lead to non-degenerate and triple-
degenerate orbitals occupied by five electrons. The latter splits due to the
$C_{3v}$ symmetric crystal field of the defective 4H-SiC lattice. Finally,
these defects states constitute an orbital singlet ${}^{4}A_{2}(g)$ ground
state and an orbital triplet ${}^{4}T_{2}(e)$ excited state, where the latter
splits to ${}^{4}A_{2}(e)$ and ${}^{4}E(e)$ states in ascending order for the
reason as quoted above [60]. We note that the strength of the crystal field
and the energy spacing between these levels depends on the actual defect site
and in 4H-SiC the splitting is larger for the Si-vacancy defect at the
quasicubic site [61]. We continue with that Si-vacancy configuration in
4H-SiC. At low temperatures, the fluorescence is dominanted by the
${}^{4}A_{2}(e)\rightarrow{}^{4}A_{2}(g)$ optical transition which results in
the so-called V2 PL spectrum with zero-phonon-line (ZPL) wavelength at 917 nm
(1.35 eV) (see Ref. 60 and references therein). The $m_{S}=\pm 1/2$ and
$m_{S}=\pm 3/2$ states of the quartet spin slightly split by the so-called
zero-field-splitting of about 70 MHz due to the crystal field. With optical
excitation of this system, the electron spin can be pumped into the $m_{S}=\pm
1/2$ in the electronic ground state, and the photoluminescence is brighter for
the $m_{S}=\pm 1/2$ states than that for $m_{S}=\pm 3/2$ states. The origin of
the spin-selective fluorescence comes from the spin-selective intersystem
crossing between the ${}^{4}A_{2}(e)$ state and the series of spin doublet
excited states lying between the quartet states [62, 63, 64, 65, 66, 67, 68,
69, 70], see also Fig. 1(b). At zero external magnetic field, radiofrequency
magnetic fields can rotate the electron spin in the ground state manifold.
This electron spin resonance frequency can be increased to microwave region
upon applying an appropriate external magnetic field aligned with the c-axis
(defect symmetry axis or crystal stacking axis, see Fig. 1(a)) of 4H-SiC.

The neutral divacancy [71, 29, 72, 73, 74, 75] in SiC consists of neighbouring
Si and C vacancies in the SiC lattice [see Fig. 1(c)]. The electronic
structure is identical to the NV centre in diamond, with C3v symmetry and a
$S=1$ electronic spin, so that spin-conserving cyclic transition between
${}^{3}A_{2}\rightarrow^{3}E$ can be used for spin-photon interfacing [32].
Difference from the NV centre are the emission wavelength in the near-infrared
(with zero-phonon lines around 1030-1130nm) and a zero-field splitting of
about $1.3$ GHz. Experimental progress on the divacancy has been quite fast
with several breakthroughs, such as long spin coherence time, single-shot
electron spin readout [54] and control of associated nuclear spins [49]
demonstrated in just a few years.

Another configuration of interest is an electron with $S=1/2$ within a doublet
orbital state. This provides altogether $2\times 2$ quantum states that split
into two doubly degenerate Kramers states due to spin-orbit coupling. The
Kramers degeneracy can be further split by magnetic fields. Neutral vanadium
substituting the silicon in the SiC forms such a system. The in-gap defect
states come from the vanadium $d$ orbitals, which are five-fold degenerate
under spherical symmetry. The crystal field provided by the SiC crystalline
lattice splits these $d$ orbitals into a low-energy orbital doublet – which
interacts weakly with the lattice – and an orbital triplet higher in energy
that hybridizes with the neighboring carbon orbitals. This orbital triplet is
further split into a doublet and a singlet due to the $C_{3v}$ symmetry of the
crystal field. In the neutral vanadium center the lower-energy double
degenerate in-gap state is occupied by a single electron which manifests the
${}^{2}E(g)$ ground state. The strength of the spin-orbit splitting in the
${}^{2}E(g)$ state depends on the specific defect site which is as large as
529 GHz for the quasicubic configuration. The orbital triplet ${}^{2}T_{1}(e)$
excited state splits to ${}^{2}E(e)$ and ${}^{2}A_{1}(e)$ levels where the
order of these levels also depend on the defect site; the ascending order is
${}^{2}E(e)$ and ${}^{2}A_{1}(e)$ at the quasicubic site [20]. The optical
transition can be described as ${}^{2}E(e)\rightarrow{}^{2}E(g)$ which is
associated with the $\alpha$ vanadium photoluminescence (PL) center in 4H-SiC
[46, 20]. As the excited state is less localized than the ground state and the
excited state partially loses its $d$ orbital character, the radiative
lifetime occurs in the region of 100 ns [20].

A similar electronic structure and optical transition
${}^{2}E_{u}(e)\rightarrow{}^{2}E_{g}(g)$ is known for the negatively charged
silicon-vacancy PL center [76, 77, 78, 79, 80] and akin group-IV–vacancy PL
centers (see Refs. 81, 82 and references therein) in diamond, where resonant
excitation between the selected states in the ground state and optical excited
state manifolds results in a coherent population trapping, and the so-called
$\Lambda$-scheme is employed to initialize and readout the qubit state [83,
84]. The most developed control and realization of the SPI have been
demonstrated for the negatively charged silicon-vacancy PL centers among the
diamond group-IV–vacancy PL centers [85, 86, 87, 88, 89, 90, 23]. This center
has a ZPL at 738 nm (1.68 eV) which requires a conversion to the
telecommunication wavelengths for efficient entanglement distribution over
optical fibers [91]. Based on the similarities in the nature of optical
transitions of the diamond silicon-vacancy PL center and the $\alpha$ vanadium
PL center, the $\Lambda$-scheme can be carried out to realize the SPI [see
Fig. 1(d)]. It comes with a significant advantage over the diamond group-
IV–vacancy centers, as the $\alpha$ center’s ZPL at 1278 nm (0.97 eV) falls
into the telecommunication O-band, removing the need for complex and
inefficient nonlinear wavelength conversion systems. We note that standard
SMF-28 telecom fibers enable single-mode propagation both for O- and C-band
photons: this is practically very convenient as the (largely unoccupied)
O-band can be used for the single-photon-level quantum channel, and the C-band
for the required classical channel, avoiding cross-talk.

Single-photon emission from vanadium PL centers in SiC has been observed [34,
35], where the interpretation of the fine structure PL requires the details of
the vanadium hyperfine interaction with the electron spin and the double
degenerate orbital [92, 93]. The interaction of the magnetic field with this
system is a complex interplay between the electron-phonon coupling, spin-orbit
coupling and the specific selection rules of the $d$ orbitals of vanadium
[94]. Understanding the fine details of the spin Hamiltonian was an inevitable
step to design quantum optics protocol for optical control of the vanadium
nuclear spin [92, 95, 96]. The observed $T_{1}$ time reaches 25 s at 100 mK
[96] which enabled to characterize the hyperfine level structure of the
$\alpha$ center via two-photon magneto-spectroscopy. For ensemble $\alpha$
centers, the observed spin dephasing $T_{2}^{*}$ time from Ramsey interference
measurements is 7.2 $\mu$s at 2 K (Ref. 97). The observed 150 counts/s from
single vanadium emitters [35] may be substantially improved by engineering the
single vanadium defects into solid immersion lenses [98], photonic crystals or
optical waveguides and open microcavities [99, 100, 101]. These parameters and
properties make $\alpha$ vanadium center in 4H-SiC very promising candidate to
realize a practical SPI with a programmable nuclear spin quantum memory.

We note that the single vanadium centers were created in SiC by vanadium ion
implantation, followed by high-temperature annealing to repair lattice damage
of the crystal lattice [34, 35]. The residual parasitic defects after
annealing may create strain and fluctuating charge environment upon
illumination. This is an important issue in securing stable emission from
single vanadium centers and produce indistinguishable quantum emitters for
quantum communication. The fluctuating charges may be flushed by integrating
the vanadium centers into p-i-n junction of 4H-SiC and applying an appropriate
electric field on it, a method which is already established for isolated
divacancy qubits [102]. A recent study on single vanadium centers in 4H-SiC
has shown that the photostability of single $\alpha$ centers upon illumination
can be significantly improved by compensating the residual n-type and p-type
dopants of SiC and pinning the Fermi-level to the middle of the band gap [35].

###  II.2 SiC devices

SiC is a mature platform for microelectronics, in particular for power
application. Capitalising on a wider bandgap, higher thermal conductivity, and
larger critical electric field than silicon, SiC devices can operate at higher
temperatures, higher current density, and higher blocking voltage and are
becoming more and more widespread in applications such as power conversion in
electric vehicles [103, 104]

Recently, researchers have started exploring SiC applications beyond power
devices [105, 106]. While it is not a material widely utilised in photonics
applications, it exhibits quite promising optical properties [107]. Due to its
wide bandgap, SiC features a large transparency range, between 0.37 - 5.6
$\mu$m for the 4H polytype [108, 109, 110].

SiC also features quite strong nonlinear coefficients, not far from values
reported for silicon and lithium niobate. The quadratic nonlinearity
$\chi^{(2)}$ has been measured to be $\approx$ 12.5 pm/V in the hexagonal
polytypes [111], while the third order (Kerr) nonlinearity $\chi^{(3)}$ is
about 6.9$\times 10^{-19}$m2/W at 1550 nm [112] for 4H-SiC. Strong nonlinear
coefficients are crucial to implement on-chip modulators and frequency
converters [113, 114, 115, 116].

Given its outstanding electronic and photonic properties, SiC provides a
formidable platform for integration of different functionalities into the same
chip. One could envision a single quantum photonic chip integrating SPI’s with
all the photonic elements required to process quantum states of light (such as
optical modulators, beamsplitters, etc), all electrically controlled.

One crucial step for high-rate spin-photon interfacing is to enhance light-
matter interaction with an optical cavity. Enhancement of light-matter
interactions in cavities can broadly be divided into two approaches: on the
one hand, cavities can increase the photon emission from defects into a
desired spatial mode, on the other hand a cavity can enhance interaction of an
incoming light pulse with the optical dipole. We will briefly describe both
approaches below.

The enhancement factor for the spontaneous emission into the cavity, $F_{SE}$
is given by

$F_{SE}=\frac{3}{4\pi^{2}}\Upsilon\frac{\gamma_{ZPL}}{\gamma_{tot}}\zeta^{2},\text{with
}\Upsilon=\left(\frac{\lambda}{n}\right)^{3}\frac{Q}{V},$ (1)

with the free-space wavelength $\lambda$ , the refractive index of the
material $n$, the quality factor $Q$, and the mode volume $V$. We have
furthermore defined the optical enhancement factor $\Upsilon$ which collects
the performance parameters of the cavity. The value $\zeta\in[0,1]$ gives the
overlap of the defect’s dipole with the electric field mode, relating both to
the relative orientation of the dipole and its position within the spatial
distribution of the mode, while $\gamma_{ZPL}$ and $\gamma_{tot}$ are the
decay rate into the zero-phonon line and the total decay rate, respectively
[117, 118].

Further, an incoming light pulse will interact more strongly with the optical
dipole transition of the defect if it is placed in a suitable cavity. If
transitions of different spin states can be resolved, the latter mechanism can
be implemented for spin-dependent absorption, reflection, or phase shifting of
the incoming light. For a symmetric, lossless cavity, the fractions of the
resonant optical power reflected and transmitted by the coupled system are
given by [119]

$R_{C}=\left(\frac{2C}{2C+1}\right)^{2}\,\text{ and
}\,T_{C}=\left(\frac{1}{2C+1}\right)^{2},$ (2)

where $C=F_{SE}/2$ is the cooperativity of the system. For finite
cooperativity, a fraction of the light will be scattered and lost by the
system and is given by $S_{C}=4C/(2C+1)^{2}$. Such scattering processes can
further lead to undesired spin flips. These expressions assume low-power
excitation, i.e. far below the saturation power of the system.

The last few years have seen great progress in the development of SiC
microcavities [10, 107]. An important starting point is the fabrication of
thin SiC membranes. Few-microns thick membranes on a high-reflectivity
Distributed Bragg Reflector (DBR) can be used for open microcavities,
positioning a second concave DBR on top of the emitter [120]. Thinner
suspended membranes (few hundred nanometers thick) are required to fabricate
photonic crystal devices such as photonic crystal nanocavities and nanobeams.
Seminal papers have demonstrated the fabrication of membranes and cavities
[99, 121, 122, 123] by electro-chemical etching, exploiting the etching
selectivity between regions of different doping. More recently, researchers
have developed thin-film SiC on insulator, by bonding SiC on a SiO2-on-Si
wafer, and grinding/polishing the SiC to the desired thickness [10]. This
technique can deliver wafer-scale thin-film SiC with low roughness, and has
been used to fabricate different types of microcavities [124, 125]. However,
the yield in such processes is currently hampered by non-uniformity of the SiC
thickness, leading to low yield in photonic device fabrication.

SiC photonic crystal cavities have reached extremely high quality factors of
$6.3\times 10^{5}$ while maintaining a small mode volume of
$2.1\left(\lambda/n\right)^{3}$, corresponding to $\Upsilon=3\times 10^{5}$
[126]. While no integration with Fabry-Pérot resonators has been reported for
SiC, devices using membranes of other materials have yielded promising
results. As an example, a Fabry-Pérot microcavity containing an yttrium
orthosilicate (YSO) membrane reached $\Upsilon=7\times 10^{3}$ [127].
Recently, microcavities with smaller mode volume and higher finesse have been
demonstrated, indicating that $\Upsilon=2\times 10^{4}$ could be reached for
SiC [120]. While the enhancement factor is expected to be lower than for
optimized photonic crystal cavities, Fabry-Pérot microcavities offer highly
efficient coupling to single-mode fibers and integration with micro-electro-
mechanical systems for individual tuning in large-scale systems [21].

From a combination of measurements and _ab-initio_ calculations, vanadium on
the $\alpha$ site of 4H SiC is expected to have a branching ratio of
$\gamma_{ZPL}/\gamma_{tot}\simeq 9\,\%$ [20], giving $C$ approaching 100 for
the best reported Fabry-Pérot microcavities, and even approaching 1000 for the
best reported photonic crystal cavities, respectively. In both cases, a high
contrast between coupled and uncoupled spin states can be expected.

##  III Beyond point-to-point quantum key distribution with SiC devices

In the following, we will focus on applying SiC devices in quantum key
distribution (QKD), which is arguably the most mature family of quantum
communication protocols. This approach is particularly useful, since the
performance of SiC devices in quantum networks can now be assessed and
optimized based on a single parameter, namely the secure key-rate (SKR) in
QKD, which is the rate of distributed bits that can be used for encryption
purposes. The SKR can be used as an overall performance parameter of quantum
networks, since it not only depends on the achievable throughput of photons,
but also crucially on errors during transmission. In direct transmission, the
limiting factors of the SKR are the achievable photon repetition rate of the
source and the time resolution of the detection system, whereas the SKR in
memory-enhanced quantum networks is mainly limited by the processing time,
communication latency and efficiency of the quantum nodes as will be discussed
in this chapter.

The two parties involved in QKD, called Alice and Bob, exchange secret keys in
an information-theoretic secure way. Typically, the secret key is encoded in
two randomly chosen conjugate bases by Alice, and only Bob can obtain the key
by randomly measuring in the same conjugate bases. Due to the no-cloning
theorem [3, 4], a third party is fundamentally incapable to obtain the key
without prior knowledge of Alice’s or Bob’s basis settings. All eavesdropping
attempts disturb the quantum state and signal the presence of an adversary.
There are two families of QKD protocols. In the prepare-and-measure type (e.g.
the BB84 protocol [128]), Alice prepares the quantum states and sends them to
Bob, who performs measurements. Entanglement-based protocols (e.g. the BBM92
protocol [129]) consist of a central node which distributes pairs of entangled
photons to Alice and Bob, both of which perform measurements on their received
photon.

Practical implementations of QKD over long distances are mainly impeded by
photon loss in optical fiber. The loss of photons leads to an exponential
decrease of the secure key rate with fiber distance, limiting the maximal key
exchange distance to a few hundred km in optical fiber [130]. This is the case
for a direct fiber connection between Alice and Bob. An alternative approach
is the division of the total distance between Alice and Bob into several
segments. The loss in each of these segments is now exponentially reduced,
which overall leads to a substantial improvement in the secure key rate
between Alice and Bob. There are two fundamentally different approaches which
make use of this segmentation. The first approach is known as a trusted
repeater, where each of the nodes connecting two segments performs a full QKD
protocol and the resulting key is relayed to other segments. While this indeed
increases the possible transmission distance indefinitely, each node reads out
the key, which necessitates absolute trust in each node. The second approach
is known as a quantum repeater [8]. Here, adjacent nodes are supplied with
entangled photons which are stored in quantum memories. Once the quantum
memories of all nodes are loaded, nested entanglement swapping is performed in
order to entangle the end nodes which belong to Alice and Bob. With
entanglement at hand, Alice and Bob can now perform any quantum communication
protocol using entanglement as a resource.

SiC devices are natural candidates for this purpose, since quantum repeater
stations must facilitate the storage of qubits over long periods of time and
process stored qubits for entanglement distillation [131]. Despite their
potential, current SiC devices, as well as other quantum memory platforms, are
unable to fulfill the stringent requirements of quantum repeaters, let alone
the necessary error correction or entanglement distillation overheads, and
therefore fail to outperform direct transmission of photons. However, there
are QKD protocols which exhibit a quantum memory enhancement without requiring
a full-fledged quantum repeater chain [27, 132].

Within the scope of this white paper, we want to focus on one particular
protocol, so-called memory-assisted measurement-device-independent QKD (MA-
MDI-QKD) [26], which requires only a single quantum repeater node. At first,
we cover the deployment of SiC devices as quantum nodes and discuss to what
extent they fulfill the requirements for quantum communication. We then go
through the MA-MDI-QKD protocol in greater detail and simulate the protocol
based on realistic parameters of state-of-the-art SiC devices. Additionally,
we discuss the opportunities of SiC devices for advanced quantum network
architectures.

###  III.1 SiC devices as quantum nodes

Figure 2: SiC device configuration enabling a heralded quantum memory and an
asynchronous Bell state measurement. The time-bin state of an incoming photon
is converted into spin-photon entanglement between the SiC defect electron
spin and an outgoing time-bin encoded photon. A measurement of the outgoing
photon in an imbalanced Mach-Zehnder interferometer with imbalance $\Delta t$
teleports the state of the initial photon into the spin state of the SiC
defect, heralded by a single-photon detection.

SiC devices serve as an SPI, allowing the quantum state of a photon to be
transferred to an electronic spin state, and vice versa. A device
configuration implementing this interface is sketched in Fig. 2 and discussed
below. After the qubit is stored in the spin state, we can apply arbitrary
unitary operations using microwave pulses. To connect two quantum links, we
need to perform at least two-qubit gates in the quantum node.

The SPI primarily relies on spin-photon entanglement. Let us consider the
writing process of a photonic qubit state into the quantum memory. We use a
time-bin encoding of the photon, although it is worth noting that SiC memories
can also be connected to other degrees of freedom, like the polarization
domain [22]. A time-bin qubit

$\ket{\Phi_{\text{Photon}}}=\frac{1}{\sqrt{2}}\left(\ket{t_{0}}+\text{e}^{i\phi}\ket{t_{1}}\right),$
(3)

is realized as a coherent superposition of two orthogonal states, namely the
presence of a photon at time $t_{0}$ and at a later time $t_{1}$. The electron
spin is initialized in state

$\ket{\Psi}_{\text{Spin}}^{\text{init}}=\frac{1}{\sqrt{2}}\left(\ket{\downarrow}+\ket{\uparrow}\right),$
(4)

where $\ket{\downarrow}$ ($\ket{\uparrow}$) corresponds to the spin down (up)
state of the electron. Based on the non-degenerate level structure [133], a
photon arriving at time $t_{0}$ is now only resonant with the optical
transition of state $\ket{\downarrow}$ and is thus reflected off the defect-
cavity system, resulting in the joint spin-photon state $\ket{\downarrow
t_{0}}$. Between $t_{0}$ and $t_{1}$, a $\pi$-pulse is applied to the
microwave transition, which inverts the electron spin state from
$\ket{\downarrow}$ to $\ket{\uparrow}$ and vice versa. The later time-bin
$\ket{t_{1}}$ is now resonant with the optical transition of state
$\ket{\uparrow}$, and upon successful reflection results in state
$\ket{\uparrow t_{1}}$. Both the population transfer between the electronic
spin states and the time-bin state are coherent processes, which results in a
coherent superposition of the spin-photon states

$\ket{\Psi}_{\text{Spin-photon}}=\frac{1}{\sqrt{2}}\left(\ket{\downarrow
t_{0}}+\text{e}^{i\phi}\ket{\uparrow t_{1}}\right),$ (5)

describing a spin-photon-entangled state. An optical circulator now redirects
the reflected photons into a detection unit, which consists of a Mach-Zehnder
interferometer with imbalance $\Delta t=t_{1}-t_{0}$ and single-photon
detectors (see Fig.2). This Mach-Zehnder interferometer realises a
probabilistic measurement in the X-basis
$\\{1/\sqrt{2}(\ket{t_{0}}+\ket{t_{1}}),1/\sqrt{2}(\ket{t_{0}}-\ket{t_{1}})\\}$.
A measurement of the photon in this basis transfers or teleports the initial
photon state onto the spin state, resulting in

$\ket{\Psi}_{\text{Spin}}^{\text{final}}=\frac{1}{\sqrt{2}}\left(\ket{\downarrow}+\text{e}^{i\phi}\ket{\uparrow}\right),$
(6)

where the measurement-induced phase ambiguity, resulting from the
probabilistic registration in one of the two single-photon detectors after the
Mach-Zehnder interferomter, has already been compensated 111Without loss of
generality we assume that the compensation is performed immediately after the
photon measurement. In a quantum communication setting, the compensation will
not be performed immediately since unitary operations on the spin are time-
consuming. Instead, the measurement outcome is stored and classically
communicated at a later time.. The detection of a single photon after the
interferometer therefore heralds the successful writing process of the initial
photon state into the spin state memory. The overall efficiency of the writing
process is limited to a maximum of 25%. This is because the state-dependent
reflection of the photon fails in 50% of the cases, and the projective
measurement in the Mach-Zehnder interferometer also fails in 50% of the cases
[135].

Two-qubit gates play a crucial role in quantum communication, especially for
achieving a BSM between two incoming photons. SiC devices provide a suitable
approach to perform this BSM asynchronously using a single defect [23]. After
writing the first photon in the spin memory, a second photon with phase
$\phi^{\prime}$ can be loaded into the same defect memory. The resulting spin
state

$\ket{\Psi}_{\text{Spin}}^{\text{BSM}}=\frac{1}{\sqrt{2}}\left(\ket{\downarrow}+\text{e}^{i(\phi+\phi^{\prime})}\ket{\uparrow}\right),$
(7)

inherits the sum of the phases of both photons. Once more, the phase ambiguity
that arises after photon measurement has already been compensated for. The BSM
is concluded by reading out the spin state in the X-basis. Depending on the
measurement outcome, two Bell states, namely the $\Phi^{+}$ or the $\Phi^{-}$
state, can be discriminated. While the asynchronous BSM is resource efficient
– only a single quantum memory is required – both photons enter the cavity via
the same single-mode fiber. To prevent additional losses caused by
probabilistic routing with a beamsplitter [23], one can opt for active optical
switching instead.

###  III.2 Memory-assisted measurement-device-independent QKD

Figure 3: Comparison between different QKD schemes. a) In prepare-and-measure-
type QKD protocols (e.g., BB84), Alice produces quantum states and sends them
to Bob, who performs measurements. b) In measurement-device-independent
(MDI)-QKD protocols, Alice and Bob each prepare quantum states and send them
to Charlie, an untrusted third party. Charlie performs a Bell state
measurement (BSM) on both quantum states and based on the outcome of this
measurement, Alice and Bob agree on a secret key. c) In memory-assisted
measurement-device-independent (MA-MDI)-QKD, both Alice and Bob produce
quantum states and send them to Charlie. Prior to the BSM, Charlie
synchronises the arrival of the quantum states with the help of quantum
memories (QM). Upon successful Bell state measurement (BSM), Charlie announces
the outcome of the measurement which leads to the establishment of a secret
key between Alice and Bob.

Measurement-device-independent (MDI) QKD can be viewed as an entanglement-
based QKD protocol in reverse. In entanglement-based QKD a central source
produces pairs of entangled photons and transmits them to the communicating
parties Alice and Bob. In MDI QKD, both Alice and Bob randomly and
independently prepare photons in one of the four BB84 states [128] and send
them to a third, untrusted party, called Charlie (C) (see Fig. 3). Charlie
performs a BSM which projects the separable state of Alice’s and Bob’s photon
on a joint state in the Bell basis. After C announces the outcome of the BSM,
Alice and Bob announce the bases of their respective BB84 state {$\ket{0}$,
$\ket{1}$, $1/\sqrt{2}(\ket{0}\pm\ket{1})$}. Depending on the announcement,
Alice or Bob either swap the bit value in their record or keep them as they
are to make sure their bits are always correlated. This protocol is
measurement-device-independent, since it avoids known side-channel attacks and
vulnerabilities of the detectors [136]. The protocol requires that both
Alice’s and Bob’s photon arrive simultaneously at the BSM. With increasing
channel loss, the probability of two photons arriving simultaneously decreases
exponentially. For this reason, MDI-QKD does not scale favorably compared to
direct transmission.

Nonetheless, the protocol’s efficiency can be significantly bolstered through
the preliminary storage of photons at the central node before the BSM. The
photon storage can serve the vital function of synchronizing the channels
between Alice and Bob [26]. This alleviates the need for precise simultaneous
photon arrival. The BSM is executed asynchronously, exclusively upon the
complete loading of both memories. In essence, this scheme merges ideas from
quantum repeaters and MDI-QKD and is thus among the simplest QKD protocols
involving quantum memories.

The asynchronous BSM introduced in the last section is perfectly suited for
MA-MDI-QKD with some slight adaptations. Since both Alice’s and Bob’s photon
must be guided to the same SiC device, some kind of optical switching must be
employed. An efficient solution to this problem is to use two SiC devices and
an optical switch which re-routes the fibers after the first detection event
(see Fig. 4). This toggling prevents the node C from being idle and is a first
step towards parallelization (see Sec. IV). This is one crucial technological
step beyond the first demonstration of a memory-assisted QKD protocol in Ref.
[23], where the authors employ a probabilistic routing of the photons.

Figure 4: Two SiC devices receiving photons from Alice and Bob via an optical
switch. Each of the SiC devices can perform asynchronous Bell state
measurements. In order to avoid idle times of the node, the optical switch
toggles Alice’s and Bob’s fibers after successful detection of one photon
either from Alice or Bob.

###  III.3 Results and main limitations

In this section we will analyze the key parameters of SiC devices and their
impact on the performance of quantum nodes in MA-MDI-QKD. Along with link
loss, the primary factor limiting the SKR over long distances is the
combination of the photon rate, time resolution, and dark count rate of the
single-photon detectors [137]. Unlikely events in which an undetected photon
projects the spin state, while two further photons are detected, are not
considered.

For memory-assisted QKD to surpass the direct point to point key rate, the
advantages gained from using quantum memories must outweigh the costs in
efficiency, processing time, and fidelity associated with realistic SiC
devices. Hence, we focus on parameters critical to the performance of the
asynchronous BSM. To achieve a high SKR, efficiency, fidelity, communication
latencies, and processing time are the most important factors to consider. In
App. A, we provide a set of values for the most important parameters that are
used in our simulations. Chiefly, we assume high cooperativity resulting in
unit contrast for the two different spin states.

Based on our previous analysis, we have determined that the memory writing
success rate has a lower limit of 25%, resulting in a maximum achievable
efficiency of 6.5% for the asynchronous BSM. This sets a fundamental baseline,
but the SiC-cavity system itself introduces additional imperfections,
including a finite cooperativity of the cavity, leading to further losses.
Other factors contributing to losses include the quantum efficiencies of the
single-photon detectors and the insertion losses of the optical switch and
optical circulator. Although the fidelity of the spin read-out is generally
high [27], the fidelity of the spin-photon entanglement used in the writing
process is significantly lower. This lower fidelity arises from the
involvement of single-photon interference as a heralding mechanism.

Writing a photonic qubit into the quantum memory presents a time-consuming
process when compared to the timescales of photon sources, which typically
operate in the GHz regime. The primary constraint arises from the microwave
pulse employed to perform unitary operations on the electron spin. The
duration of a $\pi$-pulse, denoted as $\tau_{\pi}$, determines the minimum
separation between the time-bins of a qubit $\Delta t$, requiring $\Delta
t>\tau_{\pi}$. Due to the probabilistic heralding measurement, photons are
detected outside their initial temporal qubit space. Consequently, the time-
bin separation of a single qubit also restricts the spacing between two
successive time-bin qubits. Thus, the photon repetition rate of the QKD
transmitter is bounded by $1/(2\tau_{\pi})$, where a typical $\pi$-pulse
duration of $\tau_{\pi}=$100\text{\,}\mathrm{ns}$$ yields a maximum photon
repetition rate of 5 MHz. Furthermore, the photon repetition rate incurs an
additional penalty resulting from the temporal spread of the time-bins
$\tau_{p}=$11.2\text{\,}\mathrm{ns}$$, which is constrained by the bandwidth
of the quantum memory as determined by the time-bandwidth product of a
transform-limited pulse. Including this contribution, the photon repetition
rate is ultimately bounded by
$1/(2\tau_{\pi}+2\tau_{p})=$4.5\text{\,}\mathrm{MHz}$$. Once a successful BSM
is heralded, the readout of the electron spin necessitates a microwave
$\pi/2$-pulse and re-initialization of the spin followed by a second
$\pi/2$-pulse, rendering the electron spin unavailable during this interval.
Similarly, the electron needs to be reset and rotated into a superposition
once the memory time has elapsed.

Figure 5: MA-MDI-QKD implemented with realistic SiC devices and varying
$\pi$-pulse durations $\tau_{\pi}$. Secure key rates are plotted as a function
of transmission distance through a single-mode optical fiber (Corning SMF-28).
The solid lines correspond to different $\pi$-pulse durations of the electron
spin, which are inversely related to the achievable photon repetition rate of
the protocol with a dephasing time $T_{2}=$10\text{\,}\mathrm{ms}$$. The BB84
and the MDI-QKD protocols are also plotted at different photon repetition
rates (4.5 MHz and 5 GHz). Three distinct regions can be identified based on
different secure key rate versus distance scalings. In Region I, the
implemention of MA-MDI-QKD with SiC devices outperforms point-to-point QKD.
Region II is dominated by dephasing of the electron spins, while region III is
dominated by noise induced by accidental coincidence counts. The secure key
rates are calculated in the asymptotic limit.

The strong influence of the $\pi$-pulse duration on the SKR can be observed in
Fig. 5. We simulated the secure key rate in MA-MDI-QKD for four different
$\pi$-pulse durations
$($10\text{\,}\mathrm{ns}$,$25\text{\,}\mathrm{ns}$,$50\text{\,}\mathrm{ns}$$
and $$100\text{\,}\mathrm{ns}$)$, as a function of the link distance in
standard telecommunication fibers (Corning SMF-28). Here it can be seen that
one of the primary factors limiting the rate of long-distance quantum
communication is the sequence duration for spin-photon generation, which is
limited by the $\pi$-pulse duration of the electron spin and, to a lesser
extent, by the optical bandwidth of the spin-dependent response of the cavity-
defect system. Shorter $\pi$-pulses would result in key rates which could
easily outperform a point-to-point communication, even for short-distance
links. For comparison purposes, we simulated the MDI-QKD protocol (dashed
lines) and the BB84 protocol (dash-dotted line) along with the MA-MDI-QKD
protocol (solid lines). Two different photon repetition rates were employed in
simulating each of the protocols that are not assisted by quantum memories.
The lower photon repetition rate (4.5 MHz) corresponds to the $\pi$-pulse-
limiting rate of MA-MDI-QKD, while the higher photon repetition rate (5 GHz)
corresponds to the scenario, where the time-resolution of the detectors is the
limiting factor. Similar to the photon repetition rates, also the resulting
SKR differ by three orders of magnitude, indicating the huge potential of an
increased photon repetition rate.

The efficiency-penalty of our implementation of the MA-MDI protocol can be
observed at a fiber distance of 0 km. While the memory-assisted protocol
should result in the same rate as the MDI protocol at zero transmission loss,
there is still a difference in the SKR due to the different efficiencies of
the BSM (6.5% in MA-MDI-QKD compared to 50% in MDI-QKD).

Figure 6: MA-MDI-QKD implemented with realistic SiC devices and varying
dephasing times $T_{2}$. Secure key rates are plotted as a function of
transmission distance through a single-mode optical fiber (Corning SMF-28).
The solid lines correspond to different dephasing times of the electron spin
with a $\pi$-pulse duration $\tau_{\pi}=$100\text{\,}\mathrm{ns}$$. The BB84
and the MDI-QKD protocols are also plotted at different photon repetition
rates (4.5 MHz and 5 GHz). The secure key rates are calculated in the
asymptotic limit.

In general, the SKR in MA-MDI-QKD exhibits three distinct scalings, which are
separated by dashed vertical lines in Fig. 5. In region I, the scaling of the
SKR with fiber distance is dominated by the utilization of a quantum memory.
This is the region, where the memory-assisted protocol outperforms point-to-
point QKD protocols. In region II, the scaling of the SKR with fiber distance
is dominated by decoherence. Here, the distances and the accompanying losses
become large enough, such that the quantum states stored in the electron spin
start to decohere according to a specific dephasing process [26], rendering
the quantum memory useless. The resulting key-over-distance-scaling is now
similar to the scaling of MDI-QKD, where both photons are required to arrive
simultaneously at the central node. In region III, the scaling of the SKR with
fiber distance is dominated by accidental coincidences, which is accompanied
by a rapid decrease of the SKR towards zero. Accidental coincidences arise
from dark counts of the heralding detectors, which are counts that are not
triggered by an incoming photon. This ultimately limits the maximal achievable
communication distance in any QKD protocol.

Memory-assisted quantum networks demand long storage times. On the other hand,
they are required due to low transmission probabilities inherent to long-
distance quantum links and the resulting synchronization times of the two
incoming photons. Another noteworthy limitation of MA-MDI-QKD therefore
pertains to the dephasing of the electron spin. If the dephasing time of the
defect is exceeded, the memory must be re-initialized, resulting in the loss
of the stored qubit and detrimentally impacting the achievable communication
distance. While this predicament could be circumvented by transferring the
state from the electron spin to the long-lived nuclear spin, typical
conversion times fall within the microsecond regime and the nuclear spins do
not couple to the cavity mode, rendering quantum registers impractical for
this protocol.

In Fig. 6, the dephasing time $T_{2}$ of the spin defect assumes the values 10
ms, 100 ms, 1 s and 10 s. The region where the scaling is dephasing-limited
(region II) shifts to longer transmission distances with increasing dephasing
time. Specifically, a tenfold increase of the dephasing time results roughly
in additional $50\text{\,}\mathrm{km}$ of maximal transmission distance.
Therefore, prolonging dephasing times to $T_{2}\gg 100\,$ms would be an
important step to significantly outperform point-to-point QKD protocols
operating at optimal photon repetition rate.

A further bottleneck of our proposed scheme is the low yield of the writing
process, constrained by a 25% upper limit, which sets a fundamental baseline
for the efficiency of the asynchronous Bell state measurement in its current
implementation. This efficiency limit can be eliminated via two measures.
Firstly, the heralding measurement for teleporting the photonic qubit into the
spin qubit in its current form employs a passive and imbalanced Mach-Zehnder
interferometer. Due to the probabilistic nature of the interferometer, half of
the photons are lost. One can replace the passive interferometer by an
actively-switched interferometer which, given sufficiently low insertion loss,
can mitigate this photon loss. Secondly, in the scheme described above, only
photons which are reflected off the cavity are post-selected on. By including
the transmitted photons, projections on other Bell states can be utilized,
avoiding this photon loss channel.

Addtionally, multiplexing techniques, such as wavelength multiplexing, which
are common in modern telecommunication networks, can be harnessed for
achieving higher rates in quantum networks. Wavelength multiplexing in fiber
networks is highly standardized, with plenty of cheap off-the-shelf
components. The SiC platform is ideally suited for wavelength multiplexing due
to the high level of integration possible with silicon micro-electro-
mechanical systems and the resulting frequency tunability of each cavity. In
Fig. 7, the SKR in MA-MDI-QKD is plotted with 172-fold multiplexing, leading
to 172-fold increase of the SKR. We assume 88 wavelength channels and
additional two-fold multiplexing in the polarization degree of freedom. While
only a single optical fiber is required between the communicating parties, the
resources required at the nodes scale linearly with the number of multiplexed
channels.

Finally, it should be mentioned that photon losses could be further reduced by
utilizing a different optical frequency. The photon loss at the
telecommunication O-band ($\sim$ 0.3 dB/km), investigated here, is much lower
than at optical wavelengths emitted from other defect platforms [138].
However, the band with the lowest loss, which is primarily used in optical
telecommunication systems nowadays, is the C-band, with a loss of $\sim$ 0.2
dB/km. While the difference between these two bands is seemingly small, it
accumulates to an order of magnitude loss difference after 100 km of
propagation.

Figure 7: MA-MDI-QKD implemented with realistic SiC devices, varying
$\pi$-pulse durations $\tau_{\pi}$ and 172-fold multiplexing. The multiplexing
is achieved through 88 wavelength channels and two polarization channels.
Secure key rates are plotted as a function of transmission distance through a
single-mode optical fiber (Corning SMF-28). The solid lines correspond to
different $\pi$-pulse durations of the electron spin, which are inversely
related to the achievable photon repetition rate of the protocol with a
dephasing time $T_{2}=$10\text{\,}\mathrm{ms}$$. The BB84 and the MDI-QKD
protocols are also plotted at different photon repetition rates (4.5 MHz and 5
GHz). Three distinct regions can be identified based on different secure key
rate versus distance scalings. The secure key rates are calculated in the
asymptotic limit. Figure 8: Roadmap for deployment of high-performance quantum
links based on SiC photonics in the next decade. Bar ends indicate when
technological developments (materials, integration) are expected to have
reached a level suitable for large-scale deployment. Similarly, bar ends for
benchmarks indicate when a performance level sufficient for deployment on
metropolitan-scale links is achieved. Defect identification, characterization,
and development is expected to lead to continued improvements throughout this
evolution.

##  IV Roadmap for SiC quantum links

We now summarize the required technological steps for SiC photonics towards
full deployment based on the example of repeater-extended quantum
communication. In order to be competitive with competing approaches, this
target needs to be reached within the next decade (see Fig. 8). As underlined
by the preceding calculations, this application requires high-rate spin-photon
entanglement with high fidelity and long ($\gg 100\,$ms) spin coherence
lifetime, with hundreds of addressable sites at each repeater node for
multiplexing, to usefully exceed the rates provided by direct links.

####  IV.0.1 Prerequisites

Regarding materials development, the properties of most defects in SiC can be
improved by carefully controlling the properties of the host crystal [139].
Important aspects are the control of dopant density for charge state
stability, a pristine crystalline structure to avoid strain inhomogeneity and
undesired charge traps, and isotopic control to increase spin coherence as
well as to reduce inhomogeneous broadening of the optical and spin transitions
in some defects. Additionally, most if not all defects will benefit from
charge depletion, which can be achieved in diode structures. A further
necessity is the development of high-yield processes for the creation of thin,
ultrasmooth membranes with uniform, $\text{\,}\mathrm{\SIUnitSymbolMicro
m}$-scale thickness for FP microcavities and even thinner structures for PC
cavities. While proof-of-principle demonstrations of such processes have also
been performed, the yield or crystal quality of these SiC membranes have not
yet reached a sufficient level for large-scale deployment.

This development is necessary for all types of optical enhancement structures
[107], apart from very few exceptions such as bullseye ring resonators, which
can conceivably be implemented on bulk crystals but are not suitable for the
spin-dependent reflection scheme discussed above. While defects which are
spectrally and electronically stable might be utilized as emitters with
Purcell or even only collection enhancement, the type of spin-photon
interaction described above will be advantageous for most systems as it
greatly reduces defect ionization and light-induced spectral diffusion. We
underline here that defects with longer wavelength transitions benefit from
lower losses and a higher tolerance to imperfections in the photonic
enhancement structures: As an example, the loss due to interface roughness in
FP cavities decreases with $\sigma\propto 1/\lambda^{2}$, leading to a
corresponding increase of the enhancement. Only very few examples of photonic
enhancement have been reported on for SiC defects so far, making the
development of these structures an important task for the scientific
community.

All candidate defect centres will require high-fidelity spin initialization,
manipulation, and readout, and will need to reach the desired coherence times.
Additionally, high-yield creation of defects at predetermined positions in the
crystal is highly desirable for the subsequent integration into photonic
enhancement structures. In order to reduce the complexity of the multiplexing
architecture, it is furthermore desirable to tune all defects at one repeater
site to the same optical frequency so as to achieve indistinguishability. For
most defects, this requirement implies tuning by strain or electrostatic
means. Together with the requirement for fast individual spin control, this
necessity implies a high degree of integration with multiple wire structures
on the SiC surface, for which stringent limits on the power dissipation and
conductive thermal load are given by the cooling power of the cryogenic
environment. This, in turn, hints at the necessity for resonantly enhanced
and/or superconducting spin control structures.

Many of the postulated requirements imply the use of cryogenic infrastructure
for all candidate defects, though only vanadium is known to need temperatures
$<1\,$K for sufficiently long spin relaxation lifetime, while impressive
coherence times have been achieved with other defect systems at around $4\,$K.

Finally, wavelength conversion will be necessary for all known defects in SiC,
apart from the NV centre in 3C SiC [42] and most neutral vanadium defects,
which have transitions in the telecom O band. The development of compact,
scalable, and efficient converters will thus be required for most candidate
defects. Successful proof-of principle demonstrations have been achieved, but
engineering a solution that is deployable at scale remains an outstanding
task.

####  IV.0.2 Applications

Photonic quantum links with memory units are broadly seen as having four
distinct applications, which pose slightly different requirements:

Repeaters for quantum key distribution that are integrated in a global network
additionally require an efficient interface to space-based quantum
communication systems, which currently operate at visible wavelengths or in
the telecom C-band.

Photonically connected qubits or qudits within spin-based quantum computers
can be envisioned without wavelength conversion or frequency multiplexing.
Fault-tolerant architectures, however, place even greater demands on yield,
scalability, coherence, and fidelity of the SPI’s. Additionally, they can
benefit more strongly from nuclear spin ancillae than simple communication
protocols. Quantum computing architectures based on small quantum processing
units connected by a photonic channel [140], all integrated on a single SiC
chip including elements such as waveguides, Bragg filters, electrically-
controlled optical modulators for routing, etc., can be envisioned.

Further applications will be entanglement distribution for other networked
quantum computers and entanglement distribution for networked quantum sensors.
For these, interfacing between the qubits or quantum sensors and the SPI needs
to be developed.

####  IV.0.3 Prioritization

These differences notwithstanding, the overall set of requirements allows to
set priority levels for development of different aspects of the technology. We
focus here on aspects which are specifically connected to SiC devices, thereby
excluding wavelength conversion and cryogenic infrastructure, to which
advances in SiC photonics cannot contribute directly. The highest priority
should be given to materials development aspects. Most of these are
additionally beneficial to the SiC industry and to emerging applications of
classical SiC photonics, thereby providing the highest incentives overall. The
next priority is the selection of the most suitable defect for deployment, as
this determines the requirements for photonic enhancement and interoperability
with telecom networks. As several defects currently under study present
advantageous features, this decision can only be taken at a fairly late stage
of technological development. Nonetheless, several performance parameters need
to be ascertained precisely along this path, including the Debye-Waller
factor, radiative efficiency, and transition branching ratios, the spin
relaxation and coherence lifetimes, the operation temperature, as well as any
limitations on the single-spin initialization, readout, and gate times and
fidelities which could limit the SPI performance. This type of
characterization can be expected to exclude several defects from applications
in quantum photonics. However, as new candidate defects continue to emerge,
this task will remain ongoing beyond the deployment of the first devices.

For SPI benchmarking, each defect with sufficient performance parameters needs
to be incorporated in a photonic enhancement structure, replete with all
control wiring and potentially with SiC diode structures. Aside from the
enhancement factor, the main emphasis in this development must be placed on
scalability, as vast numbers of SPI’s will be required for all quantum
technology applications. A large part of these technological aspects is common
to all defects and should therefore be performed in parallel to the detailed
characterization of spin centres.

Since different applications and protocols place differing requirements on the
performance of the SPI, a global benchmark cannot be defined. Nonetheless,
certain performance indicators are common to most settings. A possible
baseline benchmark which encapsulates many of the stated requirements is the
product of the spin-photon entanglement rate and the spin coherence lifetime
at telecom wavelength and after fiber coupling. The next benchmark level is
the product of rate and lifetime of spin-spin entanglement with two such
units, which subsumes aspects such as indistinguishability and
synchronization. Both of these benchmarks need to be defined with a threshold
fidelity, or be scaled appropriately for a chosen protocol.

####  IV.0.4 Timeline

For these developments to take place within the next decade, a concerted
effort by the SiC photonics community with strong industrial participation
will be required. The payoff, however, will be large for all involved
stakeholders, and will provide technological developments with beneficial
effects far beyond the science and technology domains. While ambitious, the
timeline for these developments can be achieved assuming continued growth in
support from governments and continued advances in the burgeoning SiC
industry.

##  V Summary

We have provided an overview of SiC photonics using spin centres for quantum
links. These devices have applications in quantum computing, secure key
distribution, and as entanglement links for distributed quantum computation
and sensing. Using memory-assisted QKD as an example, we have investigated the
key parameters which determine the performance of such links, using current
state of the art parameters as a starting point.

In this study, we have undertaken a comprehensive analysis of the key
parameters of SiC devices and their impact on the performance of quantum nodes
in the context of memory-assisted measurement-device-independent-QKD. We opted
for this particular QKD protocol implementation, because it provides an
excellent platform for examining the performance of a single quantum memory by
focusing on a single parameter – the secure key rate. Importantly, the
implementation of this protocol with SiC devices includes all essential
building blocks of large-scale repeater networks. Our investigation has
revealed several crucial factors that influence the secure key rate over long
communication distances, shedding light on both the potential and limitations
of spin centers in SiC.

From there, the technological maturity of SiC fabrication, will allow for many
devices on a single SiC wafer. One possibility is to harness wavelength
multiplexing techniques [141], which is efficient up to several tens of users.
Extending this network size in a scalable fashion is feasible with active
optical switches [142]. This entails integrating many defects on a SiC chip,
which are linked by a programmable optical switch module. For example, one
could use this quantum network router as the access node in a star topology
network. Pairs of user nodes are then connected to a single SiC defect at the
access node, where an asynchronous BSM is performed. This operation is
initiated on request by two users. They can either establish a cryptographic
key or use the BSM as entangling operation, e.g., for quantum repeater
networks.

Quantum repeater networks are the ultimate goal for long-distance quantum
communication and the SiC platform is a strong candidate for serving this
purpose. This vision can only be realized once a single quantum repeater node
outperforms point-to-point quantum communication. Only then, quantum repeater
networks with several quantum repeater nodes will prove beneficial in quantum
communication and might be deployed in the field. This should also guide the
experimental efforts in SiC-based SPI’s. Therefore, the first milestone on the
roadmap towards a large-scale quantum repeater network is the demonstration of
the single-node [23] or two-node [18, 17] scenario.

While other authors are mainly concerned with beating the repeaterless bound
[143] per channel use [132, 23], we go one step further in this white paper.
We benchmark SiC devices with existing QKD technologies, which, for example,
allow higher photon repetition rates in comparison to current specifications
of SiC devices. This practical approach allows us to make statements about the
operational capability of SiC-based quantum memories in real-world quantum
networks.

Another usecase is the deployment of SiC devices for end nodes in quantum
networks. The quantum memories in end nodes delay the read-out of photonic
quantum states or re-emit stored states after certain time intervals for
various quantum information processing tasks. End nodes therefore have a
different set of requirements compared to repeater nodes. As an example, the
transfer to nuclear spins is a good option to increase the storage time of end
nodes, even though in-depth comparison to other quantum memory platforms is
necessary to evaluate the deployability of defects in SiC for this usecase.

These considerations allow to define a path towards deployment of SiC
photonics for high-performance quantum links, which we outlined in IV. We
project that, with a concerted effort of the scientific community and the SiC
industry, it will be possible to achieve this goal within the end of the
decade.

##  VI Acknowledgements

This work was performed with funding support from the European Union’s Horizon
2020 research and innovation programme under grant agreement No 862721
QuanTELCO.

## References

  * Wehner  _et al._ [2018] S. Wehner, D. Elkouss, and R. Hanson, Quantum internet: A vision for the road ahead, Science 362, eaam9288 (2018).
  * Zhang and Zhuang [2021] Z. Zhang and Q. Zhuang, Distributed quantum sensing, Quantum Science and Technology 6, 043001 (2021).
  * Park [1970] J. L. Park, The concept of transition in quantum mechanics, Foundations of physics 1, 23 (1970).
  * Wootters and Zurek [1982] W. K. Wootters and W. H. Zurek, A single quantum cannot be cloned, Nature 299, 802 (1982).
  * Lu  _et al._ [2022] C.-Y. Lu, Y. Cao, C.-Z. Peng, and J.-W. Pan, Micius quantum experiments in space, Rev. Mod. Phys. 94, 035001 (2022).
  * Liao  _et al._ [2018] S.-K. Liao, W.-Q. Cai, J. Handsteiner, B. Liu, J. Yin, L. Zhang, D. Rauch, M. Fink, J.-G. Ren, W.-Y. Liu, Y. Li, Q. Shen, Y. Cao, F.-Z. Li, J.-F. Wang, Y.-M. Huang, L. Deng, T. Xi, L. Ma, T. Hu, L. Li, N.-L. Liu, F. Koidl, P. Wang, Y.-A. Chen, X.-B. Wang, M. Steindorfer, G. Kirchner, C.-Y. Lu, R. Shu, R. Ursin, T. Scheidl, C.-Z. Peng, J.-Y. Wang, A. Zeilinger, and J.-W. Pan, Satellite-relayed intercontinental quantum network, Phys. Rev. Lett. 120, 030501 (2018).
  * Ecker  _et al._ [2023] S. Ecker, J. Pseiner, J. Piris, and M. Bohmann, Advances in entanglement-based QKD for space applications, in  _International Conference on Space Optics — ICSO 2022_, Vol. 12777, edited by K. Minoglou, N. Karafolas, and B. Cugny, International Society for Optics and Photonics (SPIE, 2023) p. 1277727.
  * Briegel  _et al._ [1998] H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, Quantum repeaters: The role of imperfect local operations in quantum communication, Physical Review Letters 81, 5932 (1998).
  * DiVincenzo [2000] D. P. DiVincenzo, The physical implementation of quantum computation, Fortschritte der Physik: Progress of Physics 48, 771 (2000).
  * Lukin  _et al._ [2020] D. M. Lukin, M. A. Guidry, and J. Vučković, Integrated quantum photonics with silicon carbide: challenges and prospects, PRX Quantum 1, 020102 (2020).
  * Dréau  _et al._ [2018] A. Dréau, A. Tchebotareva, A. E. Mahdaoui, C. Bonato, and R. Hanson, Quantum frequency conversion of single photons from a nitrogen-vacancy center in diamond to telecommunication wavelengths, Phys. Rev. Appl. 9, 064031 (2018).
  * Tchebotareva  _et al._ [2019] A. Tchebotareva, S. L. Hermans, P. C. Humphreys, D. Voigt, P. J. Harmsma, L. K. Cheng, A. L. Verlaan, N. Dijkhuizen, W. de Jong, A. Dréau, and R. Hanson, Entanglement between a diamond spin qubit and a photonic time-bin qubit at telecom wavelength, Physical Review Letters 123, 10.1103/physrevlett.123.063601 (2019).
  * Rakonjac  _et al._ [2021] J. V. Rakonjac, D. Lago-Rivera, A. Seri, M. Mazzera, S. Grandi, and H. de Riedmatten, Entanglement between a telecom photon and an on-demand multimode solid-state quantum memory, Phys. Rev. Lett. 127, 210502 (2021).
  * Hammerer  _et al._ [2010] K. Hammerer, A. S. Sørensen, and E. S. Polzik, Quantum interface between light and atomic ensembles, Rev. Mod. Phys. 82, 1041 (2010).
  * Y ılmaz  _et al._ [2010] S. T. Y ılmaz, P. Fallahi, and A. Imamoğlu, Quantum-dot-spin single-photon interface, Phys. Rev. Lett. 105, 033601 (2010).
  * Lodahl [2017] P. Lodahl, Quantum-dot based photonic quantum networks, Quantum Science and Technology 3, 013001 (2017).
  * Lago-Rivera  _et al._ [2021] D. Lago-Rivera, S. Grandi, J. V. Rakonjac, A. Seri, and H. de Riedmatten, Telecom-heralded entanglement between multimode solid-state quantum memories, Nature 594, 37 (2021).
  * Liu  _et al._ [2021] X. Liu, J. Hu, Z. F. Li, X. Li, P. Y. Li, P. J. Liang, Z. Q. Zhou, C. F. Li, and G. C. Guo, Heralded entanglement distribution between two absorptive quantum memories, Nature 594, 41 (2021).
  * Krutyanskiy  _et al._ [2023] V. Krutyanskiy, M. Galli, V. Krcmarsky, S. Baier, D. A. Fioretto, Y. Pu, A. Mazloom, P. Sekatski, M. Canteri, M. Teller, J. Schupp, J. Bate, M. Meraner, N. Sangouard, B. P. Lanyon, and T. E. Northup, Entanglement of trapped-ion qubits separated by 230 meters, Phys. Rev. Lett. 130, 050803 (2023).
  * Spindlberger  _et al._ [2019] L. Spindlberger, A. Csóré, G. Thiering, S. Putz, R. Karhu, J. Hassan, N. Son, T. Fromherz, A. Gali, and M. Trupke, Optical properties of vanadium in 4 h silicon carbide for quantum technology, Physical Review Applied 12, 10.1103/physrevapplied.12.014015 (2019).
  * Derntl  _et al._ [2014] C. Derntl, M. Schneider, J. Schalko, A. Bittner, J. Schmiedmayer, U. Schmid, and M. Trupke, Arrays of open, independently tunable microcavities, Optics Express 22, 22111 (2014).
  * Vasconcelos  _et al._ [2020] R. Vasconcelos, S. Reisenbauer, C. Salter, G. Wachter, D. Wirtitsch, J. Schmiedmayer, P. Walther, and M. Trupke, Scalable spin–photon entanglement by time-to-polarization conversion, npj Quantum Information 6, 10.1038/s41534-019-0236-x (2020).
  * Bhaskar  _et al._ [2020] M. K. Bhaskar, R. Riedinger, B. Machielse, D. S. Levonian, C. T. Nguyen, E. N. Knall, H. Park, D. Englund, M. Lončar, D. D. Sukachev, and M. D. Lukin, Experimental demonstration of memory-enhanced quantum communication, Nature 580, 60 (2020).
  * Pompili  _et al._ [2021] M. Pompili, S. L. Hermans, S. Baier, H. K. Beukers, P. C. Humphreys, R. N. Schouten, R. F. Vermeulen, M. J. Tiggelman, L. dos Santos Martins, B. Dirkse, _et al._ , Realization of a multinode quantum network of remote solid-state qubits, Science 372, 259 (2021).
  * Bersin  _et al._ [2023] E. Bersin, M. Sutula, Y. Q. Huan, A. Suleymanzade, D. R. Assumpcao, Y.-C. Wei, P.-J. Stas, C. M. Knaut, E. N. Knall, C. Langrock, _et al._ , Telecom networking with a diamond quantum memory, arXiv preprint arXiv:2307.08619 (2023).
  * Panayi  _et al._ [2014] C. Panayi, M. Razavi, X. Ma, and N. Lütkenhaus, Memory-assisted measurement-device-independent quantum key distribution, New Journal of Physics 16, 10.1088/1367-2630/16/4/043005 (2014).
  * Azuma  _et al._ [2023] K. Azuma, S. E. Economou, D. Elkouss, P. Hilaire, L. Jiang, H.-K. Lo, and I. Tzitrin, Quantum repeaters: From quantum networks to the quantum internet, Rev. Mod. Phys. 95, 045006 (2023).
  * Janzén  _et al._ [2001] E. Janzén, A. Henry, J. P. Bergman, A. Ellison, and B. Magnusson, Material characterization need for SiC-based devices, Materials Science in Semiconductor Processing Advanced Characterisation of Semiconductor Materials, 4, 181 (2001).
  * Gali  _et al._ [2010] A. Gali, A. Gällström, N. T. Son, and E. Janzén, Theory of Neutral Divacancy in SiC: A Defect for Spintronics, Materials Science Forum 645-648, 395 (2010).
  * Christle  _et al._ [2015] D. J. Christle, A. L. Falk, P. Andrich, P. V. Klimov, J. U. Hassan, N. T. Son, E. Janzén, T. Ohshima, and D. D. Awschalom, Isolated electron spins in silicon carbide with millisecond coherence times, Nature Materials 14, 160 (2015).
  * Widmann  _et al._ [2015] M. Widmann, S.-Y. Lee, T. Rendler, N. T. Son, H. Fedder, S. Paik, L.-P. Yang, N. Zhao, S. Yang, I. Booker, A. Denisenko, M. Jamali, S. A. Momenzadeh, I. Gerhardt, T. Ohshima, A. Gali, E. Janzén, and J. Wrachtrup, Coherent control of single spins in silicon carbide at room temperature, Nature Materials 14, 164 (2015).
  * Christle  _et al._ [2017] D. J. Christle, P. V. Klimov, C. F. de las Casas, K. Szász, V. Ivády, V. Jokubavicius, J. Ul Hassan, M. Syväjärvi, W. F. Koehl, T. Ohshima, N. T. Son, E. Janzén, A. Gali, and D. D. Awschalom, Isolated Spin Qubits in SiC with a High-Fidelity Infrared Spin-to-Photon Interface, Physical Review X 7, 021046 (2017).
  * Wang  _et al._ [2020a] J.-F. Wang, F.-F. Yan, Q. Li, Z.-H. Liu, H. Liu, G.-P. Guo, L.-P. Guo, X. Zhou, J.-M. Cui, J. Wang, Z.-Q. Zhou, X.-Y. Xu, J.-S. Xu, C.-F. Li, and G.-C. Guo, Coherent Control of Nitrogen-Vacancy Center Spins in Silicon Carbide at Room Temperature, Physical Review Letters 124, 223601 (2020a).
  * Wolfowicz  _et al._ [2020] G. Wolfowicz, C. P. Anderson, B. Diler, O. G. Poluektov, F. J. Heremans, and D. D. Awschalom, Vanadium spin qubits as telecom quantum emitters in silicon carbide, Science Advances 6, eaaz1192 (2020).
  * Cilibrizzi  _et al._ [2023] P. Cilibrizzi, M. J. Arshad, B. Tissot, N. T. Son, I. G. Ivanov, T. Astner, P. Koller, M. Ghezellou, J. Ul-Hassan, D. White, C. Bekker, G. Burkard, M. Trupke, and C. Bonato, Ultra-narrow inhomogeneous spectral distribution of telecom-wavelength vanadium centres in isotopically-enriched silicon carbide, Nature Communications 14, 8448 (2023).
  * Gordon  _et al._ [2015] L. Gordon, A. Janotti, and C. G. Van de Walle, Defects as qubits in 3${C}$\- and 4${H}$-SiC, Physical Review B 92, 045208 (2015).
  * von Bardeleben  _et al._ [2016] H. J. von Bardeleben, J. L. Cantin, A. Csóré, A. Gali, E. Rauls, and U. Gerstmann, NV centers in ${3C},{4H}$, and ${6H}$ silicon carbide: A variable platform for solid-state qubits and nanosensors, Physical Review B 94, 121202 (2016).
  * Csóré  _et al._ [2017] A. Csóré, H. J. von Bardeleben, J. L. Cantin, and A. Gali, Characterization and formation of NV centers in ${3C},{4H}$, and ${6H}$ SiC: An ab initio study, Physical Review B 96, 085204 (2017).
  * Wang  _et al._ [2020b] J.-F. Wang, Z.-H. Liu, F.-F. Yan, Q. Li, X.-G. Yang, L. Guo, X. Zhou, W. Huang, J.-S. Xu, C.-F. Li, and G.-C. Guo, Experimental Optical Properties of Single Nitrogen Vacancy Centers in Silicon Carbide at Room Temperature, ACS Photonics 7, 1611 (2020b).
  * Mu  _et al._ [2020] Z. Mu, S. A. Zargaleh, H. J. von Bardeleben, J. E. Fröch, M. Nonahal, H. Cai, X. Yang, J. Yang, X. Li, I. Aharonovich, and W. Gao, Coherent Manipulation with Resonant Excitation and Single Emitter Creation of Nitrogen Vacancy Centers in 4H Silicon Carbide, Nano Letters 20, 6142 (2020).
  * Murzakhanov  _et al._ [2021] F. F. Murzakhanov, B. V. Yavkin, G. V. Mamin, S. B. Orlinskii, H. J. von Bardeleben, T. Biktagirov, U. Gerstmann, and V. A. Soltamov, Hyperfine and nuclear quadrupole splitting of the NV- ground state in ${4H}$-SiC, Physical Review B 103, 245203 (2021).
  * Jurgen von Bardeleben  _et al._ [2021] H. Jurgen von Bardeleben, J.-L. Cantin, U. Gerstmann, W. G. Schmidt, and T. Biktagirov, Spin Polarization, Electron–Phonon Coupling, and Zero-Phonon Line of the NV Center in 3C-SiC, Nano Letters 21, 8119 (2021).
  * Narahara  _et al._ [2021] T. Narahara, S.-i. Sato, K. Kojima, Y. Hijikata, and T. Ohshima, Influences of hydrogen ion irradiation on n${}_{\text{c}}$v${}_{\text{si}}^{-}$ formation in 4H-silicon carbide, Applied Physics Express 14, 021004 (2021).
  * Schneider  _et al._ [1990] J. Schneider, H. D. Müller, K. Maier, W. Wilkening, F. Fuchs, A. Dörnen, S. Leibenzeder, and R. Stein, Infrared spectra and electron spin resonance of vanadium deep level impurities in silicon carbide, Applied Physics Letters 56, 1184 (1990).
  * Kaufmann  _et al._ [1995] B. Kaufmann, A. Dörnen, and F. S. Ham, Zeeman Spectroscopy and Crystal-Field Model of Neutral Vandium in 6H-Silicon Carbide, Materials Science Forum 196–201, 707 (1995).
  * Baur  _et al._ [1997] J. Baur, M. Kunzer, and J. Schneider, Transition Metals in SiC Polytypes, as Studied by Magnetic Resonance Techniques, physica status solidi (a) 162, 153 (1997).
  * Falk  _et al._ [2015] A. L. Falk, P. V. Klimov, V. Ivády, K. Szász, D. J. Christle, W. Koehl, A. Gali, and D. D. Awschalom, Optical Polarization of Nuclear Spins in Silicon Carbide, Physical Review Letters 114, 247603 (2015).
  * Ivády  _et al._ [2016] V. Ivády, P. V. Klimov, K. C. Miao, A. L. Falk, D. J. Christle, K. Szász, I. A. Abrikosov, D. D. Awschalom, and A. Gali, High-Fidelity Bidirectional Nuclear Qubit Initialization in SiC, Physical Review Letters 117, 220503 (2016).
  * Bourassa  _et al._ [2020] A. Bourassa, C. P. Anderson, K. C. Miao, M. Onizhuk, H. Ma, A. L. Crook, H. Abe, J. Ul-Hassan, T. Ohshima, N. T. Son, G. Galli, and D. D. Awschalom, Entanglement and control of single nuclear spins in isotopically engineered silicon carbide, Nature Materials 19, 1319 (2020).
  * Robledo  _et al._ [2011] L. Robledo, L. Childress, H. Bernien, B. Hensen, P. F. A. Alkemade, and R. Hanson, High-fidelity projective read-out of a solid-state spin quantum register, Nature 477, 574 (2011).
  * Nagy  _et al._ [2019] R. Nagy, M. Niethammer, M. Widmann, Y.-C. Chen, P. Udvarhelyi, C. Bonato, J. U. Hassan, R. Karhu, I. G. Ivanov, N. T. Son, J. R. Maze, T. Ohshima, O. O. Soykal, A. Gali, S.-Y. Lee, F. Kaiser, and J. Wrachtrup, High-fidelity spin and optical control of single silicon-vacancy centres in silicon carbide, Nature Communications 10, 1954 (2019).
  * Yin  _et al._ [2013] C. Yin, M. Rancic, G. G. de Boo, N. Stavrias, J. C. McCallum, M. J. Sellars, and S. Rogge, Optical addressing of an individual erbium ion in silicon, Nature 497, 91 (2013).
  * Zhang  _et al._ [2021] Q. Zhang, Y. Guo, W. Ji, M. Wang, J. Yin, F. Kong, Y. Lin, C. Yin, F. Shi, Y. Wang, and J. Du, High-fidelity single-shot readout of single electron spin in diamond with spin-to-charge conversion, Nature Communications 12, 1529 (2021).
  * Anderson  _et al._ [2022] C. P. Anderson, E. O. Glen, C. Zeledon, A. Bourassa, Y. Jin, Y. Zhu, C. Vorwerk, A. L. Crook, H. Abe, J. Ul-Hassan, T. Ohshima, N. T. Son, G. Galli, and D. D. Awschalom, Five-second coherence of a single spin with single-shot readout in silicon carbide, Science Advances 8, eabm5912 (2022).
  * Fang  _et al._ [2023] R.-Z. Fang, X.-Y. Lai, T. Li, R.-Z. Su, B.-W. Lu, C.-W. Yang, R.-Z. Liu, Y.-K. Qiao, C. Li, Z.-G. He, J. Huang, H. Li, L.-X. You, Y.-H. Huo, X.-H. Bao, and J.-W. Pan, Experimental generation of spin-photon entanglement in silicon carbide (2023), arXiv:2311.17455 [quant-ph] .
  * Taminiau  _et al._ [2012] T. H. Taminiau, J. J. T. Wagenaar, T. van der Sar, F. Jelezko, V. V. Dobrovitski, and R. Hanson, Detection and control of individual nuclear spins using a weakly coupled electron spin, Phys. Rev. Lett. 109, 137602 (2012).
  * Bradley  _et al._ [2019] C. E. Bradley, J. Randall, M. H. Abobeih, R. C. Berrevoets, M. J. Degen, M. A. Bakker, M. Markham, D. J. Twitchen, and T. H. Taminiau, A ten-qubit solid-state spin register with quantum memory up to one minute, Phys. Rev. X 9, 031045 (2019).
  * Cramer  _et al._ [2016] J. Cramer, N. Kalb, M. A. Rol, B. Hensen, M. S. Blok, M. Markham, D. J. Twitchen, R. Hanson, and T. H. Taminiau, Repeated quantum error correction on a continuously encoded qubit by real-time feedback, Nature Communications 7, 11526 (2016).
  * Parthasarathy  _et al._ [2023] S. K. Parthasarathy, B. Kallinger, F. Kaiser, P. Berwian, D. B. Dasari, J. Friedrich, and R. Nagy, Scalable quantum memory nodes using nuclear spins in silicon carbide, Phys. Rev. Appl. 19, 034026 (2023).
  * Janzén  _et al._ [2009] E. Janzén, A. Gali, P. Carlsson, A. Gällström, B. Magnusson, and N. Son, The silicon vacancy in SiC, Physica B: Condensed Matter 404, 4354 (2009).
  * Ivády  _et al._ [2017] V. Ivády, J. Davidsson, N. T. Son, T. Ohshima, I. A. Abrikosov, and A. Gali, Identification of Si-vacancy related room-temperature qubits in ${4H}$ silicon carbide, Physical Review B 96, 161114 (2017).
  * Baranov  _et al._ [2011] P. G. Baranov, A. P. Bundakova, A. A. Soltamova, S. B. Orlinskii, I. V. Borovykh, R. Zondervan, R. Verberk, and J. Schmidt, Silicon vacancy in SiC as a promising quantum system for single-defect and single-photon spectroscopy, Physical Review B 83, 125203 (2011).
  * Gali [2012] A. Gali, Excitation spectrum of point defects in semiconductors studied by time-dependent density functional theory, Journal of Materials Research 27, 897 (2012).
  * Riedel  _et al._ [2012] D. Riedel, F. Fuchs, H. Kraus, S. VĂ¤th, A. Sperlich, V. Dyakonov, A. A. Soltamova, P. G. Baranov, V. A. Ilyin, and G. V. Astakhov, Resonant Addressing and Manipulation of Silicon Vacancy Qubits in Silicon Carbide, Physical Review Letters 109, 226402 (2012).
  * Soltamov  _et al._ [2012] V. A. Soltamov, A. A. Soltamova, P. G. Baranov, and I. I. Proskuryakov, Room Temperature Coherent Spin Alignment of Silicon Vacancies in ${4H}$\- and ${6H}$-SiC, Physical Review Letters 108, 226402 (2012).
  * Soykal  _et al._ [2016] O. O. Soykal, P. Dev, and S. E. Economou, Silicon vacancy center in ${4H}$-SiC: Electronic structure and spin-photon interfaces, Physical Review B 93, 081207 (2016).
  * Soykal and Reinecke [2017] O. O. Soykal and T. L. Reinecke, Quantum metrology with a single spin-$\frac{3}{2}$ defect in silicon carbide, Physical Review B 95, 081405 (2017).
  * Dong  _et al._ [2019] W. Dong, M. W. Doherty, and S. E. Economou, Spin polarization through intersystem crossing in the silicon vacancy of silicon carbide, Physical Review B 99, 184102 (2019).
  * Widmann  _et al._ [2019] M. Widmann, M. Niethammer, D. Y. Fedyanin, I. A. Khramtsov, T. Rendler, I. D. Booker, J. Ul Hassan, N. Morioka, Y.-C. Chen, I. G. Ivanov, _et al._ , Electrical charge state manipulation of single silicon vacancies in a silicon carbide quantum optoelectronic device, Nano letters 19, 7173 (2019).
  * Wang  _et al._ [2021] J.-F. Wang, F.-F. Yan, Q. Li, Z.-H. Liu, J.-M. Cui, Z.-D. Liu, A. Gali, J.-S. Xu, C.-F. Li, and G.-C. Guo, Robust coherent control of solid-state spin qubits using anti-Stokes excitation, Nature Communications 12, 3223 (2021).
  * Son  _et al._ [2006] N. T. Son, P. Carlsson, J. ul Hassan, E. Janzén, T. Umeda, J. Isoya, A. Gali, M. Bockstedte, N. Morishita, T. Ohshima, and H. Itoh, Divacancy in 4H-SiC, Physical Review Letters 96, 055501 (2006).
  * Gali [2011] A. Gali, Time-dependent density functional study on the excitation spectrum of point defects in semiconductors, physica status solidi (b) 248, 1337 (2011).
  * Koehl  _et al._ [2011] W. F. Koehl, B. B. Buckley, F. J. Heremans, G. Calusine, and D. D. Awschalom, Room temperature coherent control of defect spin qubits in silicon carbide, Nature 479, 84 (2011).
  * Ivády  _et al._ [2019] V. Ivády, J. Davidsson, N. Delegan, A. L. Falk, P. V. Klimov, S. J. Whiteley, S. O. Hruszkewycz, M. V. Holt, F. J. Heremans, N. T. Son, D. D. Awschalom, I. A. Abrikosov, and A. Gali, Stabilization of point-defect spin qubits by quantum wells, Nature Communications 10, 5607 (2019).
  * Li  _et al._ [2022] Q. Li, J.-F. Wang, F.-F. Yan, J.-Y. Zhou, H.-F. Wang, H. Liu, L.-P. Guo, X. Zhou, A. Gali, Z.-H. Liu, _et al._ , Room-temperature coherent manipulation of single-spin qubits in silicon carbide with a high readout contrast, National Science Review 9, nwab122 (2022).
  * Sternschulte  _et al._ [1994] H. Sternschulte, K. Thonke, R. Sauer, P. C. Münzinger, and P. Michler, 1.681-eV luminescence center in chemical-vapor-deposited homoepitaxial diamond films, Physical Review B 50, 14554 (1994).
  * Goss  _et al._ [1996] J. P. Goss, R. Jones, S. J. Breuer, P. R. Briddon, and S. Öberg, The Twelve-Line 1.682 eV Luminescence Center in Diamond and the Vacancy-Silicon Complex, Physical Review Letters 77, 3041 (1996).
  * Neu  _et al._ [2011] E. Neu, D. Steinmetz, J. Riedrich-Müller, S. Gsell, M. Fischer, M. Schreck, and C. Becher, Single photon emission from silicon-vacancy colour centres in chemical vapour deposition nano-diamonds on iridium, New Journal of Physics 13, 025012 (2011).
  * Gali and Maze [2013] A. Gali and J. R. Maze, Ab initio study of the split silicon-vacancy defect in diamond: Electronic structure and related properties, Physical Review B 88, 235205 (2013).
  * Hepp  _et al._ [2014] C. Hepp, T. Müller, V. Waselowski, J. N. Becker, B. Pingault, H. Sternschulte, D. Steinmüller-Nethl, A. Gali, J. R. Maze, M. Atatüre, and C. Becher, Electronic Structure of the Silicon Vacancy Color Center in Diamond, Physical Review Letters 112, 036405 (2014).
  * Thiering and Gali [2018] G. Thiering and A. Gali, Ab Initio Magneto-Optical Spectrum of Group-IV Vacancy Color Centers in Diamond, Physical Review X 8, 021063 (2018).
  * Ruf  _et al._ [2021] M. Ruf, N. H. Wan, H. Choi, D. Englund, and R. Hanson, Quantum networks based on color centers in diamond, Journal of Applied Physics 130, 070901 (2021).
  * Pingault  _et al._ [2014] B. Pingault, J. N. Becker, C. H. H. Schulte, C. Arend, C. Hepp, T. Godde, A. I. Tartakovskii, M. Markham, C. Becher, and M. Atatüure, All-Optical Formation of Coherent Dark States of Silicon-Vacancy Spins in Diamond, Physical Review Letters 113, 263601 (2014).
  * Rogers  _et al._ [2014] L. J. Rogers, K. D. Jahnke, M. H. Metsch, A. Sipahigil, J. M. Binder, T. Teraji, H. Sumiya, J. Isoya, M. D. Lukin, P. Hemmer, and F. Jelezko, All-Optical Initialization, Readout, and Coherent Preparation of Single Silicon-Vacancy Spins in Diamond, Physical Review Letters 113, 263602 (2014).
  * Becker  _et al._ [2016] J. N. Becker, J. Görlitz, C. Arend, M. Markham, and C. Becher, Ultrafast all-optical coherent control of single silicon vacancy colour centres in diamond, Nature Communications 7, 13512 (2016).
  * Pingault  _et al._ [2017] B. Pingault, D.-D. Jarausch, C. Hepp, L. Klintberg, J. N. Becker, M. Markham, C. Becher, and M. Atatüre, Coherent control of the silicon-vacancy spin in diamond, Nature Communications 8, 15579 (2017).
  * Sukachev  _et al._ [2017] D. D. Sukachev, A. Sipahigil, C. T. Nguyen, M. K. Bhaskar, R. E. Evans, F. Jelezko, and M. D. Lukin, Silicon-Vacancy Spin Qubit in Diamond: A Quantum Memory Exceeding 10 ms with Single-Shot State Readout, Physical Review Letters 119, 223602 (2017).
  * Becker  _et al._ [2018] J. N. Becker, B. Pingault, D. Groß, M. Gündoģan, N. Kukharchyk, M. Markham, A. Edmonds, M. Atatüre, P. Bushev, and C. Becher, All-Optical Control of the Silicon-Vacancy Spin in Diamond at Millikelvin Temperatures, Physical Review Letters 120, 053603 (2018).
  * Sohn  _et al._ [2018] Y.-I. Sohn, S. Meesala, B. Pingault, H. A. Atikian, J. Holzgrafe, M. Gündoģan, C. Stavrakas, M. J. Stanley, A. Sipahigil, J. Choi, M. Zhang, J. L. Pacheco, J. Abraham, E. Bielejec, M. D. Lukin, M. Atatüre, and M. Lonçar, Controlling the coherence of a diamond spin qubit through its strain environment, Nature Communications 9, 1 (2018).
  * Machielse  _et al._ [2019] B. Machielse, S. Bogdanovic, S. Meesala, S. Gauthier, M. J. Burek, G. Joe, M. Chalupnik, Y. I. Sohn, J. Holzgrafe, R. E. Evans, C. Chia, H. Atikian, M. K. Bhaskar, D. D. Sukachev, L. Shao, S. Maity, M. D. Lukin, and M. Loncar, Quantum Interference of Electromechanically Stabilized Emitters in Nanophotonic Devices, Physical Review X 9, 031022 (2019).
  * Bersin  _et al._ [2024] E. Bersin, M. Sutula, Y. Q. Huan, A. Suleymanzade, D. R. Assumpcao, Y.-C. Wei, P.-J. Stas, C. M. Knaut, E. N. Knall, C. Langrock, N. Sinclair, R. Murphy, R. Riedinger, M. Yeh, C. Xin, S. Bandyopadhyay, D. D. Sukachev, B. Machielse, D. S. Levonian, M. K. Bhaskar, S. Hamilton, H. Park, M. Lončar, M. M. Fejer, P. B. Dixon, D. R. Englund, and M. D. Lukin, Telecom networking with a diamond quantum memory, PRX Quantum 5, 010303 (2024).
  * Tissot and Burkard [2021] B. Tissot and G. Burkard, Hyperfine structure of transition metal defects in sic, Phys. Rev. B 104, 064102 (2021).
  * Gilardoni  _et al._ [2021] C. M. Gilardoni, I. Ion, F. Hendriks, M. Trupke, and C. H. v. d. Wal, Hyperfine-mediated transitions between electronic spin-1/2 levels of transition metal defects in SiC, New Journal of Physics 23, 083010 (2021).
  * Csóré and Gali [2020] A. Csóré and A. Gali, Ab initio determination of pseudospin for paramagnetic defects in SiC, Physical Review B 102, 241201 (2020).
  * Tissot  _et al._ [2022] B. Tissot, M. Trupke, P. Koller, T. Astner, and G. Burkard, Nuclear spin quantum memory in silicon carbide, Physical Review Research 4, 033107 (2022).
  * Astner  _et al._ [2022] T. Astner, P. Koller, C. M. Gilardoni, J. Hendriks, N. T. Son, I. G. Ivanov, J. U. Hassan, C. H. van der Wal, and M. Trupke, Vanadium in Silicon Carbide: Telecom-ready spin centres with long relaxation lifetimes and hyperfine-resolved optical transitions (2022), arXiv:2206.06240 .
  * Hendriks  _et al._ [2022] J. Hendriks, C. M. Gilardoni, C. Adambukulam, A. Laucht, and C. H. van der Wal, Coherent spin dynamics of hyperfine-coupled vanadium impurities in silicon carbide (2022), arXiv:2210.09942 .
  * Bekker  _et al._ [2023] C. Bekker, M. J. Arshad, P. Cilibrizzi, C. Nikolatos, P. Lomax, G. S. Wood, R. Cheung, W. Knolle, N. Ross, B. Gerardot, and C. Bonato, Scalable fabrication of hemispherical solid immersion lenses in silicon carbide through grayscale hard-mask lithography, Applied Physics Letters 122, 173507 (2023).
  * Bracher and Hu [2015] D. O. Bracher and E. L. Hu, Fabrication of high- <i>q</i> nanobeam photonic crystals in epitaxially grown 4h-sic, Nano Letters 15, 6202 (2015).
  * Radulaski  _et al._ [2017] M. Radulaski, M. Widmann, M. Niethammer, J. L. Zhang, S.-Y. Lee, T. Rendler, K. G. Lagoudakis, N. T. Son, E. Janzén, T. Ohshima, J. Wrachtrup, and J. Vučković, Scalable Quantum Photonics with Single Color Centers in Silicon Carbide, Nano Letters 17, 1782 (2017).
  * Babin  _et al._ [2022] C. Babin, R. Stöhr, N. Morioka, T. Linkewitz, T. Steidl, R. Wörnle, D. Liu, E. Hesselmeier, V. Vorobyov, A. Denisenko, M. Hentschel, C. Gobert, P. Berwian, G. V. Astakhov, W. Knolle, S. Majety, P. Saha, M. Radulaski, N. T. Son, J. Ul-Hassan, F. Kaiser, and J. Wrachtrup, Fabrication and nanophotonic waveguide integration of silicon carbide colour centres with preserved spin-optical coherence, Nature Materials 21, 67 (2022).
  * Anderson  _et al._ [2019] C. P. Anderson, A. Bourassa, K. C. Miao, G. Wolfowicz, P. J. Mintun, A. L. Crook, H. Abe, J. Ul Hassan, N. T. Son, T. Ohshima, and D. D. Awschalom, Electrical and optical control of single spins integrated in scalable semiconductor devices, Science 366, 1225 (2019).
  * She  _et al._ [2017] X. She, A. Q. Huang, O. Lucia, and B. Ozpineci, Review of silicon carbide power devices and their applications, IEEE Transactions on Industrial Electronics 64, 8193 (2017).
  * Kimoto [2022] T. Kimoto, High-voltage sic power devices for improved energy efficiency, Proceedings of the Japan Academy, Series B 98, 161 (2022).
  * Via  _et al._ [2023] F. L. Via, D. Alquier, F. Giannazzo, T. Kimoto, P. Neudeck, H. Ou, A. Roncaglia, S. E. Saddow, and S. Tudisco, Emerging SiC applications beyond power electronic devices, Micromachines 14, 1200 (2023).
  * Ou  _et al._ [2023] H. Ou, X. Shi, Y. Lu, M. Kollmuss, J. Steiner, V. Tabouret, M. Syväjärvi, P. Wellmann, and D. Chaussende, Novel photonic applications of silicon carbide, Materials 16, 1014 (2023).
  * Castelletto  _et al._ [2022] S. Castelletto, A. Peruzzo, C. Bonato, B. C. Johnson, M. Radulaski, H. Ou, F. Kaiser, and J. Wrachtrup, Silicon carbide photonics bridging quantum technology, ACS Photonics 9, 1434 (2022).
  * Wang  _et al._ [2013] S. Wang, M. Zhan, G. Wang, H. Xuan, W. Zhang, C. Liu, C. Xu, Y. Liu, Z. Wei, and X. Chen, 4h-sic: a new nonlinear material for midinfrared lasers, Laser Photonics Rev. 7, 831 (2013).
  * Zheng  _et al._ [2019a] Y. Zheng, M. Pu, A. Yi, X. Ou, and H. Ou, 4h-sic microring resonators for nonlinear integrated photonics, Opt. Lett. 44, 5784 (2019a).
  * Zheng  _et al._ [2019b] Y. Zheng, M. Pu, A. Yi, B. Chang, T. You, K. Huang, A. N. Kamel, M. R. Henriksen, A. A. Jørgensen, X. Ou, _et al._ , High-quality factor, high-confinement microring resonators in 4h-silicon carbide-on-insulator, Opt. Express 27, 13053 (2019b).
  * Sato  _et al._ [2009] H. Sato, M. Abe, I. Shoji, J. Suda, and T. Kondo, Accurate measurements of second-order nonlinear optical coefficients of 6h and 4h silicon carbide, J. of the Opt. Society of America B 26, 1892 (2009).
  * Guidry  _et al._ [2020] M. A. Guidry, K. Y. Yang, D. M. Lukin, A. Markosyan, J. Yang, M. M. Fejer, and J. Vučković, Optical parametric oscillation in silicon carbide nanophotonics, Optica 7, 1139 (2020).
  * Shi  _et al._ [2023] X. Shi, Y. Lu, and H. Ou, High-performance silicon carbide polarization beam splitting based on an asymmetric directional couplers for mode conversion, Optics Letters 48, 616 (2023).
  * Shi  _et al._ [2021] X. Shi, W. Fan, Y. Lu, A. K. Hansen, M. Chi, A. Yi, X. Ou, K. Rottwitt, and H. Ou, Polarization and spatial mode dependent four-wave mixing in a 4h-silicon carbide microring resonator, APL Photonics 6, 10.1063/5.0053296 (2021).
  * Yi  _et al._ [2020] A. Yi, Y. Zheng, H. Huang, J. Lin, Y. Yan, T. You, K. Huang, S. Zhang, C. Shen, M. Zhou, W. Huang, J. Zhang, S. Zhou, H. Ou, and X. Ou, Wafer-scale 4h-silicon carbide-on-insulator (4h–SiCOI) platform for nonlinear integrated optical devices, Optical Materials 107, 109990 (2020).
  * Zheng  _et al._ [2019c] Y. Zheng, M. Pu, A. Yi, X. Ou, and H. Ou, 4h-SiC microring resonators for nonlinear integrated photonics, Optics Letters 44, 5784 (2019c).
  * Chatzopoulos  _et al._ [2019] I. Chatzopoulos, F. Martini, R. Cernansky, and A. Politi, High-q/v photonic crystal cavities and qed analysis in 3c-sic, ACS Photonics 6, 1826 (2019).
  * Faraon  _et al._ [2013] A. Faraon, C. Santori, Z. Huang, K.-M. C. Fu, V. M. Acosta, D. Fattal, and R. G. Beausoleil, Quantum photonic devices in single-crystal diamond, New Journal of Physics 15, 025010 (2013).
  * Reiserer and Rempe [2015] A. Reiserer and G. Rempe, Cavity-based quantum networks with single atoms and optical photons, Rev. Mod. Phys. 87, 1379 (2015).
  * Fait  _et al._ [2021] J. Fait, S. Putz, G. Wachter, J. Schalko, U. Schmid, M. Arndt, and M. Trupke, High finesse microcavities in the optical telecom O-band, Applied Physics Letters 119, 221112 (2021).
  * Bracher  _et al._ [2017] D. O. Bracher, X. Zhang, and E. L. Hu, Selective purcell enhancement of two closely linked zero-phonon transitions of a silicon carbide color center, Proceedings of the National Academy of Sciences 114, 4060 (2017).
  * Crook  _et al._ [2020] A. L. Crook, C. P. Anderson, K. C. Miao, A. Bourassa, H. Lee, S. L. Bayliss, D. O. Bracher, X. Zhang, H. Abe, T. Ohshima, E. L. Hu, and D. D. Awschalom, Purcell Enhancement of a Single Silicon Carbide Color Center with Coherent Spin Control, Nano Letters 20, 3427 (2020).
  * Mokhtarzadeh  _et al._ [2022] M. Mokhtarzadeh, M. Carulla, R. Kozak, and C. David, Optimization of etching processes for the fabrication of smooth silicon carbide membranes for applications in quantum technology, Micro and Nano Engineering 16, 100155 (2022).
  * Yang  _et al._ [2023] J. Yang, M. A. Guidry, D. M. Lukin, K. Yang, and J. Vučković, Inverse-designed silicon carbide quantum and nonlinear photonics, Light: Science I& Applications 12, 201 (2023).
  * Lukin  _et al._ [2023] D. M. Lukin, M. A. Guidry, J. Yang, M. Ghezellou, S. Deb Mishra, H. Abe, T. Ohshima, J. Ul-Hassan, and J. Vučković, Two-Emitter Multimode Cavity Quantum Electrodynamics in Thin-Film Silicon Carbide Photonics, Physical Review X 13, 011005 (2023).
  * Song  _et al._ [2019] B.-S. Song, T. Asano, S. Jeon, H. Kim, C. Chen, D. D. Kang, and S. Noda, Ultrahigh-q photonic crystal nanocavities based on 4h silicon carbide, Optica 6, 991 (2019).
  * Merkel  _et al._ [2020] B. Merkel, A. Ulanowski, and A. Reiserer, Coherent and purcell-enhanced emission from erbium dopants in a cryogenic high-q resonator, Physical Review X 10, 041025 (2020).
  * Bennett and Brassard [2014] C. H. Bennett and G. Brassard, Quantum cryptography: Public key distribution and coin tossing, Theoretical computer science 560, 7 (2014).
  * Bennett  _et al._ [1992] C. H. Bennett, G. Brassard, and N. D. Mermin, Quantum cryptography without bell’s theorem, Physical review letters 68, 557 (1992).
  * Neumann  _et al._ [2022] S. P. Neumann, A. Buchner, L. Bulla, M. Bohmann, and R. Ursin, Continuous entanglement distribution over a transnational 248 km fiber link, Nature Communications 13, 6134 (2022).
  * Bennett  _et al._ [1996] C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, Purification of noisy entanglement and faithful teleportation via noisy channels, Physical review letters 76, 722 (1996).
  * Rozpędek  _et al._ [2019] F. Rozpędek, R. Yehia, K. Goodenough, M. Ruf, P. C. Humphreys, R. Hanson, S. Wehner, and D. Elkouss, Near-term quantum-repeater experiments with nitrogen-vacancy centers: Overcoming the limitations of direct transmission, Physical Review A 99, 10.1103/physreva.99.052330 (2019).
  * Nguyen  _et al._ [2019] C. Nguyen, D. Sukachev, M. Bhaskar, B. Machielse, D. Levonian, E. Knall, P. Stroganov, R. Riedinger, H. Park, M. Lončar, _et al._ , Quantum network nodes based on diamond qubits with an efficient nanophotonic interface, Physical review letters 123, 183602 (2019).
  * Note [1] Without loss of generality we assume that the compensation is performed immediately after the photon measurement. In a quantum communication setting, the compensation will not be performed immediately since unitary operations on the spin are time-consuming. Instead, the measurement outcome is stored and classically communicated at a later time.
  * Franson [1989] J. D. Franson, Bell inequality for position and time, Physical Review Letters 62, 2205 (1989).
  * Lo  _et al._ [2012] H.-K. Lo, M. Curty, and B. Qi, Measurement-device-independent quantum key distribution, Phys. Rev. Lett. 108, 130503 (2012).
  * Neumann  _et al._ [2021] S. P. Neumann, T. Scheidl, M. Selimovic, M. Pivoluska, B. Liu, M. Bohmann, and R. Ursin, Model for optimizing quantum key distribution with continuous-wave pumped entangled-photon sources, Physical Review A 104, 022406 (2021).
  * Awschalom  _et al._ [2018] D. D. Awschalom, R. Hanson, J. Wrachtrup, and B. B. Zhou, Quantum technologies with optically interfaced solid-state spins, Nature Photonics 12, 516 (2018).
  * Son  _et al._ [2020] N. T. Son, C. P. Anderson, A. Bourassa, K. C. Miao, C. Babin, M. Widmann, M. Niethammer, J. Ul Hassan, N. Morioka, I. G. Ivanov, F. Kaiser, J. Wrachtrup, and D. D. Awschalom, Developing silicon carbide for quantum spintronics, Applied Physics Letters 116, 190501 (2020), https://pubs.aip.org/aip/apl/article-pdf/doi/10.1063/5.0004454/14532891/190501_1_online.pdf .
  * Nickerson  _et al._ [2014] N. H. Nickerson, J. F. Fitzsimons, and S. C. Benjamin, Freely scalable quantum technologies using cells of 5-to-50 qubits with very lossy and noisy photonic links, Phys. Rev. X 4, 041041 (2014).
  * Wengerowsky  _et al._ [2018] S. Wengerowsky, S. K. Joshi, F. Steinlechner, H. Hübel, and R. Ursin, An entanglement-based wavelength-multiplexed quantum communication network, Nature 564, 225 (2018).
  * Hall  _et al._ [2021] M. N. Hall, K.-T. Foerster, S. Schmid, and R. Durairajan, A survey of reconfigurable optical networks, Optical Switching and Networking 41, 100621 (2021).
  * Pirandola  _et al._ [2017] S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, Fundamental limits of repeaterless quantum communications, Nature communications 8, 15043 (2017).

##  Appendix A Parameter list for MA-MDI-QKD simulations

Here, we list all relevant parameters used for the simulations of the MA-MDI-
QKD protocol using SiC devices. The values are derived from state-of-the-art
experiments and off-the-shelf component specifications. The first part of
Table 1 lists the spin-cavity parameters, while the second part of the table
lists parameters used in the simulation.

Table 1: Parameters used in the MA-MDI-QKD simulation with SiC devices. Name |  Symbol |  Value |  Comment/Description
---|---|---|---
Amplitude decay time |  $T_{1}$ |  30s |  Amplitude decay time of the electron spin $\eta_{r}(t)=\eta_{r0}\mathrm{e}^{-t/T_{1}}$.
Coherence time |  $T_{2}$ |  10ms-10s |  Dephasing time of electron spin.
Nuclear spin amplitude decay time |  $T_{\mathrm{1N}}$ |  30s |  Amplitude decay time of the nuclear spin.
Nuclear spin coherence time |  $T_{\mathrm{2N}}$ |  $>10s$ |  Dephasing time of nuclear spin.
Spin conversion time |  $T_{\mathrm{E-N}}$ |  $10\text{\,}\mathrm{\SIUnitSymbolMicro s}$ |  Time needed for a conversion from electron spin to nuclear spin.
Spin readout time |  $\tau_{\mathrm{R}}$ |  $400\text{\,}\mathrm{ns}$ |  Time required to measure the electron spin.
$\pi$-pulse time |  $\tau_{\pi}$ |  10-100 ns |  $\pi$-pulse duration.
Initialization time |  $\tau_{\mathrm{init}}$ |  $\tau_{\mathrm{R}}+\tau_{\mathrm{\pi}}$ |  Initialization time for the electron spin.
Reflectivity $\ket{\uparrow}$ |  $\eta_{\uparrow}$ |  1 |  Reflectivity of the cavity with the spin in the $\uparrow$ state, SMF included.
Reflectivity $\ket{\downarrow}$ |  $\eta_{\downarrow}$ |  0 |  Reflectivity of the cavity with the spin in the $\downarrow$ state, SMF included.
Linewidth |  $\gamma$ |  100 MHz |  Optical Fourier-limited linewidth (FWHM), including cooperative broadening.
Pulse duration |  $\tau_{\mathrm{p}}$ |  11.2 ns |  Optical pulse duration.
Writing time |  $\tau_{\mathrm{w}}$ |  20-200 ns |  $2\left(\tau_{\mathrm{p}}+\tau_{\pi}\right)$. Time difference between the time that the beginning of the pulse arrives at the QM and the time that a successful/unsuccessful loading is declared.
Reading time |  $\tau_{\mathrm{r}}$ |  410-500 ns |  400 ns + $\tau_{\pi}$. Time difference between the time that the retrieval process is applied until the end of the pulse is out.
Writing efficiency |  $\eta_{\mathrm{w}}$ |  0.13 |  Probability to store a qubit and herald success conditioned on having a single photon at the QMs input.
Reading efficiency |  $\eta_{r0}$ |  1 |  Probability to retrieve a single photon out of the QM (right after loading t=0) conditioned on a successful loading in the past.
Single-photon detection efficiency |  $\eta_{\mathrm{SPD}}$ |  0.85 |  Superconducting nanowire single photon detector
Temporal resolution |  $t_{\mathrm{SPD}}$ |  50 ps |  Superconducting nanowire single photon detector, FWHM
Dark count rate |  $\gamma_{\mathrm{dc}}$ |  100 Hz |
Background rate |  $\gamma_{\mathrm{bg}}$ |  0 Hz |  Photonic background rate per optical mode
Channel length |  $L$ |  0 – 700 km |  $L_{\mathrm{A(B)}}$ is the channel length from Alice or Bob to the respective memory. $L=L_{\mathrm{A}}+L_{\mathrm{B}}$, where we assume equal channel length $L_{\mathrm{A}}=L_{\mathrm{B}}$.
Fibre attenuation |  $\alpha_{\mathrm{Ob}}$ |  0.3 dB/km |  At the telecom O-band
Setup misalignment probability |  $e_{\mathrm{A(B)}}$ |  0 |  Probability of a qubit flip
Error correction inefficiency |  $f$ |  1.16 |  Efficiency of the error correction code
Insertion loss fibre optical circulator |  $\eta_{\mathrm{oc}}$ |  0.8 dB |
Insertion loss fibre optical switch |  $\eta_{\mathrm{os}}$ |  0.6 dB |
Optical rise/fall time optical switch |  $t_{\mathrm{os}}$ |  8 ns |
Minimal pulse width optical switch |  $\Delta t_{\mathrm{os}}$ |  90 ns |