# Entanglement of Magnetically Levitated Massive Schrödinger Cat States by
Induced Dipole Interaction

Ryan J. Marshman  Centre for Quantum Computation and Communication Technology,
School of Mathematics and Physics, University of Queensland, Brisbane,
Queensland 4072, Australia.  Sougato Bose  University College London, The
United Kingdom  Andrew Geraci  Center for Fundamental Physics, Department of
Physics and Astronomy, Northwestern University, Evanston, USA 60208  Anupam
Mazumdar  Van Swinderen Institute, University of Groningen, 9747 AG, The
Netherlands

###### Abstract

Quantum entanglement provides a novel way to test short-distance quantum
physics in a non-relativistic regime. We provide entanglement-based protocols
to potentially test the magnetically induced dipole-dipole interaction and the
Casimir-Polder potential between the two nano-crystals kept in a Schrödinger
Cat state. Our scheme is based on the Stern-Gerlach (SG) apparatus, where we
can witness the entanglement mediated by these interactions for the nano-
crystal mass $m\sim 10^{-19}$ kg with a spatial superposition size of order
$0.1$ micron in a trap relying on diamagnetic levitation. We show that it is
possible to close the SG interferometer in position and momentum with a modest
gradient in the magnetic field.

##  I Introduction

Quantum entanglement is a critical observable that demarcates the classical
from the quantum world [1]. Entanglement provides an unquestionable quantum
signature that cannot be mimicked by any classical operation between the two
quantum systems. In fact, a well-known theorem (known as local operation and
classical communication (LOCC)) prohibits entangling the two quantum systems
that are mediated by a classical interaction [2]. After all, the Standard
Model (SM) interactions are known to be quantum, and quantum entanglement-
based protocols allow us to test how various forces of nature can be entangled
in a laboratory setup [3]. At a short distance, but still, in the infrared
(IR) regime, we can test virtual photon-induced interactions [4], such as
Coulomb, Casimir-Polder [5], and magnetically induced dipole-dipole
interaction [6].

In search for the answer to the profound question; "does gravity follows the
rules of quantum mechanics or not?" witnessing gravitationally mediated
entanglement has been proposed as a key protocol to test the quantum nature of
gravity in a laboratory [7, 8](for a related work see [9]). The scheme relies
on two masses, each prepared in a spatial superposition and placed at
distances where they couple solely gravitationally. If gravity follows the
rules of quantum interaction, and not that of a classical real-valued field,
then the two masses will entangle [8, 10, 11, 12, 13, 14]. However, to test
the quantum nature of gravity we will need heavy masses $10^{-14}-10^{-15}$kg,
and large spatial superposition of $10-100{\rm\mu m}$, with long coherence
times of $1-2$ seconds. Furthermore, one can also test the quantum origin of
gravitational interaction between quantum matter and light [15], which will
enable us to understand the spin nature of the gravitational interaction. All
these protocols are commonly known as quantum gravity-induced entanglement of
masses (QGEM) [8]. One crucial ingredient for all these experiments is to
understand the entanglement generation from the known well-established photon-
induced electromagnetic interactions. The photon-induced entanglement will
create a background that is necessary to understand before we could perform
the QGEM experiment [4, 16].

The aim of this paper will be to show that there exists a very natural
electromagnetic background which is an inevitable consequence of any neutral
nano-crystal in the presence of an external magnetic field. The external
magnetic field, which we require for trapping the nano-crystal, and eventually
creating the quantum superposition will induce a magnetic dipole to the nano-
crystal. The two nano-crystals in a quantum superposition will get entangled
by the electromagnetic interaction, and hence it will provide a dominant
background for the QGEM experiment at short distances.

The use of a Stern-Gerlach (SG) apparatus is one of the most promising
approaches towards atom interferometry [17, 18, 19, 20, 21, 22]. However, for
larger objects such as nanoparticles we can also exploit the SG properties to
create spatial superposition, see [23, 24, 25, 26, 27, 28].

Such interferometers have already been realized using atom chips [19, 20, 22],
for both half-loop [18] and full-loop [22] configurations achieving the
superposition size of $3.93$ $\mu$m and $0.38$ $\mu$m in the experimental time
of 21.45 ms and 7 ms, respectively. Based on this SG scheme there have been
theoretical studies to create even more ambitious superposition sizes [26, 27,
28]. In all these cases, the idea is to manipulate the nitrogen vacancy (NV)
center of a nano-diamond. The NV center provides a spin defect, which can be
manipulated in the presence of an external magnetic field. One can use the
spins of two adjacent interferometers to create the entanglement witness by
performing spin correlations [8, 29].

Of course, one of the key challenges is to understand numerous sources of
decoherence and noise [8, 30, 31, 32, 33, 34, 4, 35, 36]. They arise from
residual gas collisions and environmental photons, which can be attenuated by
vacuum and low-temperature technologies [37, 38]. In addition, the Humpty-
Dumpty effect [39], internal cooling of the nanodiamond to improve the spin
coherence time [40, 41, 42, 43], as well as to tackle the Majorana spin-flip,
under development [25]. Moreover, there are also a series of gravitational
channels for dephasing [36, 44]; the emission of gravitons is negligible [45],
gravity gradient noise (GGN) can be mitigated with an exclusion zone [36], and
relative acceleration can be mitigated by improving the vacuum and isolating
the experimental box as much as possible.

In this work, we will aim to understand two particular EM-induced potentials
which will inevitably entangle any two quantum systems, even if we assume that
the monopole contribution is neutralized, which is experimentally feasible
[46]. The two potentials are the Casimir-Polder (CP) potential and the dipole-
dipole (DD) potential due to induced-dipole moment in the presence of an
external magnetic field, present in the SG setup. In this paper, we will
provide a superposition scheme in a levitating setup to witness the
entanglements due to these potentials. We will show that with a modest
magnetic field gradient in the SG setup, we can measure the entanglement
witness for both CP and DD potentials for a mass of neutral nano-diamond
$m\sim 10^{-19}{\rm Kg}$, and the spatial superposition of $0.1{\rm\mu m}$.

A diamagnetic material in a magnetic trapping potential will evolve according
to the Hamiltonian

$\hat{H}=\frac{\hat{\bf{p}}^{2}}{2m}+\hbar
D\hat{S}_{z}+g_{s}\frac{e\hbar}{2m_{e}}\hat{\bf{S}}\cdot{\bf{B}}+mg\hat{y}-\frac{\chi_{\rho}m}{2\mu_{0}}{\bf{B}^{2}}$
(1)

where the first term in Eq.(10) represents the kinetic energy of the
nanodiamond, $\hat{\boldsymbol{p}}$ is the momentum operator and $m$ is the
mass of the nanodiamond. The second term represents the zero-field splitting
of the NV center with $D=(2\pi)\times 2.8~{}{\rm GHz}$, $\hbar$ is the reduced
Planck constant, and $\hat{S}_{z^{\prime}}$ is the spin component operator
aligned with the NV axis. The third term represents the interaction energy of
the NV electron spin magnetic moment with the magnetic field $\boldsymbol{B}$.
The spin magnetic moment operator
$\hat{\boldsymbol{\mu}}=-g_{s}\mu_{B}\hat{\boldsymbol{S}}$, where
$g_{s}\approx 2$ is the Landè g-factor, $\mu_{B}=e\hbar/2m_{e}$ is the Bohr
magneton and $\hat{\boldsymbol{S}}$ is the NV spin operator. The fourth term
is the gravitational potential energy, $g\approx 9.8$ ${\rm m/s^{2}}$ is the
gravitational acceleration and $\hat{\boldsymbol{z}}$ is the position operator
along the direction of gravity ($z$ axis). The final term represents the
magnetic energy of a diamagnetic material (diamond) in a magnetic field,
$\chi_{\rho}=-6.2\times 10^{-9}$ ${\rm m^{3}/kg}$ is the mass susceptibility
and $\mu_{0}$ is the vacuum permeability.

For the purpose of our scheme, we will make use of a well-known trap profile
${\bf{B}}_{T}$ given by [47]

$\displaystyle{\bf{B}}_{T}=$
$\displaystyle-\left[\frac{3a_{4}\sqrt{\frac{35}{\pi}}x^{2}y}{8y_{0}^{3}}+\frac{3a_{4}\sqrt{\frac{35}{\pi}}y\left(x^{2}-y^{2}\right)}{16y_{0}^{3}}-\frac{a_{3}\sqrt{\frac{7}{6\pi}}x^{2}}{y_{0}^{2}}+\frac{a_{2}\sqrt{\frac{15}{\pi}}y}{4y_{0}}+\frac{a_{3}\sqrt{\frac{7}{6\pi}}\left(-x^{2}-y^{2}+4z^{2}\right)}{2y_{0}^{2}}\right]\hat{x}$
$\displaystyle-\left[-\frac{3a_{4}\sqrt{\frac{35}{\pi}}xy^{2}}{8y_{0}^{3}}+\frac{3a_{4}\sqrt{\frac{35}{\pi}}x\left(x^{2}-y^{2}\right)}{16y_{0}^{3}}-\frac{a_{3}\sqrt{\frac{7}{6\pi}}xy}{y_{0}^{2}}+\frac{a_{2}\sqrt{\frac{15}{\pi}}x}{4y_{0}}\right]\hat{y}-\left[\frac{2a_{3}\sqrt{\frac{14}{3\pi}}xz}{y_{0}^{2}}\right]\hat{z}$
(2)

where $y_{0}=75~{}\mu$m is the distance from the center of the trap to the
pole pieces which help generate the trap and $a_{2}=-1.3$ T, $a_{3}=0.0183$ T,
and $a_{4}=0.72$ T determine the magnetic field strength. We will take the
particle at time $t=0$ to be at rest in the trapping potential, with an
initial spin state
$\frac{1}{\sqrt{2}}\left(\left|+1\right\rangle+\left|-1\right\rangle\right)$.
The trapping potential is given by $U=(\chi_{\rho}mB^{2}/2\mu_{0})+mgy$, since
$\chi<0$, the particle can be trapped at a frequency
$\omega_{\zeta}=\sqrt{-(\chi/2\rho\mu_{0})(\partial^{2}B^{2}/\partial\zeta^{2})}$,
where $\zeta=x,y,z$.

A large gradient, linear magnetic field $\vec{B}_{P}$ is then pulsed on, for a
short time $t_{p}$ which acts to create a momentum difference correlated with
the internal spin state of the particle. The particle then evolves in the
weakly trapping potential for some time $t_{T}$ before the large gradient
linear magnetic field is again turned on for a further time $t_{P}$. At this
point, the particle should be returned to its initial position at time
$t=2t_{P}+t_{T}\equiv T$, with the internal spin state now in the form
$\frac{1}{\sqrt{2}}\left(e^{i\phi_{+}}\left|+1\right\rangle+e^{-\phi_{-}}\left|-1\right\rangle\right)$
where the phases $\phi_{\pm}$ are a result of the interactions with external
sources.

To create the superposition we will first assume the pulsed magnetic field is
linear over the region experienced by the particle, with a profile

${\bf{B}}_{p}=\eta\left(y(t=0)-y\right)\hat{y}+\eta z\hat{z}$ (3)

where $\eta$ gives the magnetic field gradient and $y(t=0)$ is the initial
position of the particle in the $y$ direction, which is away from the minimum
of the potential for the particle. We wish to start high up in the potential
to gain large momentum, which will help the two spin states to get separated
in $z$-direction as much as possible. With this definition of the pulse field,
it makes a minimal disruption to the trapping field, being zero magnitudes
(although non-zero gradient) at the particle’s location ($x=0$, $y\approx
y(t=0)$, and $z\approx 0$).

We can control the average magnitude of the diamagnetically induced magnetic
field of the diamond by initially displacing the particle in the $y$
direction. This will result in the diamond oscillating in the $y$ direction
according to the trapping frequency in this direction. This trapping frequency
in the $y$ direction will be much faster than that in the $z$ (splitting)
direction as the particle is intended to be more confined in this direction.
This oscillation is seen in Figure 1(b) which shows an example space-time
trajectory for each arm of the interferometer if it is allowed to oscillate
for a full period before the pulsed magnetic field is re-applied to close the
spatial superposition. The dual oscillatory behavior is due to the mass not
occupying the ground state of the trapping potentials in both $y$ and $z$
directions, with the $y$ trapping frequency in the $z$ direction, i.e.
$\omega_{y}\ll\omega_{z}$.

(a) Simplified interferometer arrangement.

(b) Space-time trajectory of single interferometer.

(c) Trajectory in the $z-y$ plane.

(d) Trajectory in the $x-y$ plane.

Figure 1: 1(a) shows a schematic representation of the manner in which two of
these devices can be arranged, offset by a distance $d$ in the $x$ direction
to enable the generation of entanglement between the two particles.1(b) shows
and actual space-time trajectory for a two $z$ oscillation interferometer.
1(c) shows the same trajectory in the $y-z$ plane and the trapping magnetic
field while 1(d) shows the same trajectory in the $x-y$ plane, for an
interferometer distance $d=20$ $\mu$m. All trajectories are for $m=3.8\times
10^{-19}$ kg masses, a magnetic field gradient pulse time $t_{p}\approx
160~{}\mu$s and the particle is started at $y(t=0)=-1.11~{}\mu$m.

To ensure that both the spatial wavefunction completely matches at time $t=T$,
it is necessary to ensure the trapping frequency in the $y$ direction is an
integer multiple of that in the $z$ direction such that both the position and
momentum matches at the final time. It will also be necessary to ensure the
pulsed magnetic field opening and closing the superposition matches in both
magnitude and pulse time, with deviations from this leading to reduced
contrast in the form of decoherence in the final spin states.

The pulse time $t_{p}=2\pi/\omega$ is determined by the pulsed magnetic field
gradient, $\eta$, to ensure the maximum momentum difference is induced between
the two masses, we are interested in a quarter of the oscillation period or
$t_{p}/4=\pi/(2\omega)$, where the frequency is given by the diamagnetic-
induced magnetic field $\omega=\sqrt{k/m}$, where $k$ is the spring constant
determined by the effective potential of the crystal,
$U_{\pm}(y)=-(\chi_{\rho}m/2\mu_{0})\eta^{2}y^{2}$

$t_{p}=\frac{\pi}{2\eta}\sqrt{\frac{-\mu_{0}}{2\chi_{\rho}}}$ (4)

This time is a quarter of the oscillation period of the Harmonic trap caused
by the pulsed magnetic field

All results were numerical simulations of the classical equations of motion
derived from the Hamiltonian given in Eq. 10. The magnetic profile used was
${\bf{B}}={\bf{B}}_{T}+{\bf{B}}_{p}(t)$ where ${\bf{B}}_{T}$ is given by Eq.
13 and ${\bf{B}}_{p}(t)=0$ any time the linear gradient pulse is switched off,
otherwise it is given by Eq. 14. Thus, the pulsed magnetic field was taken to
be switched on and off instantly.

Note that, as shown in Figure 1(c), due to the downward shift of the rest
position of the mass in the background magnetic field due to the downward pull
of gravity, the zero-field region of the magnetic field can be avoided by
simply initializing the mass away from it. This serves the dual purpose of
generating the induced diamagnetic field in the particle and naturally
avoiding Majorana spin flips.

Once, we have created one superposition in a trapping potential given by Eq.
(A), we can imagine bringing two such trapping potentials, hence bringing two
interferometers close to each other at a distance $d$ shown in Fig. (1(a)),
separated by a distance $d$. This is the parallel setup of the original QGEM
proposal, studied in [33, 3, 48].

If two such interferometers are placed near one another, separated in the $x$
direction by a distance $d$ with the direction the spatial splitting parallel
as shown in Figure 1(a), we expect the joint state to evolve to

$\displaystyle\left|\Psi\right\rangle=$
$\displaystyle\frac{1}{2}\left(\left|+1,+1\right\rangle+\left|-1,-1\right\rangle\right)$
$\displaystyle+\frac{e^{i\Delta\phi}}{2}\left(\left|+1,-1\right\rangle+\left|-1,+1\right\rangle\right)$
(5)

where $\Delta\phi=\phi_{+-}-\phi_{++}$ and $\phi_{ij}$ is the phase due to the
interaction between the $i$ and $j$ arms of the interferometer. We refer to
this phase difference $\Delta\phi$ as the entanglement phase, which is
actually the summation of all particle-particle interactions, as considered
separately in the following section.

Now, we are able to experimentally probe many interesting questions, such as
various particle-particle interactions mediated by photons, which may be
witnessed via the entanglement phase. These may include Casimir-Polder (cp),
and induced dipole-dipole (dd), assuming that our crystal is charged neutral
(experimentally feasible [46]). Depending on the chosen experimental
parameters, it’s likely that at least one of these interactions will be
negligible, indeed, we will consider a situation where only the dd interaction
produces a significant effect, with the cp interaction serving as the primary
background. The potentials for each interaction are given by

$\displaystyle U_{cp}(d)=$ $\displaystyle-\frac{23\hbar
c}{4\pi}\frac{\varepsilon-1}{\varepsilon+2}\frac{\left(\frac{3m}{4\pi\rho}\right)^{2}}{d^{7}}$
(6) $\displaystyle U_{dd}(d)=$
$\displaystyle\frac{2\chi_{\rho}^{2}m^{2}\left|\vec{B}(x)\right|^{2}}{4\pi\mu_{0}d^{3}}$
(7)

where $m,~{}\rho,\chi_{\rho}$ and $\varepsilon$ are the particle’s mass,
density, and magnetic mass susceptibility respectively and $d$ is the center
of the mass distance between the particles. Note that we consider the magnetic
field across the particles to be approximately constant and given by the
magnetic field at the centre of mass. These interactions $i$ will each give
rise to an entanglement phase given by

$\Delta\phi_{i}=\frac{1}{\hbar}\int_{0}^{T}\textrm{d}t~{}U_{i}\left(d_{1}(t)\right)-U_{i}\left(d_{2}(t)\right)$
(8)

where $d_{1}(t)$ ($d_{2}(t)$) is the furthest (closest) separation distance
between the two particles due to the two superposed spatial states.

The entanglement can then be found by measuring an entanglement witness, such
as see [49]

$\mathcal{W}_{i}=1-\left(2e^{-\frac{1}{2}\left(\Gamma_{n}+\Gamma_{d}\right)}\sin\left(\Delta\phi_{i}\right)+\frac{1}{2}\left(e^{-2\Gamma_{n}-\Gamma_{d}}+1\right)\right)$
(9)

where $\Gamma_{d}$ and $\Gamma_{n}$ are the damping and noise decoherence
respectively [49]. Note that as defined here, this decoherence is defined as
the decoherence rate multiplied by interferometer time. We plot the witness
${\cal W}_{dd}$ with regards to total decoherence and damping rate:
$\Gamma=\Gamma_{d}+\Gamma_{n}$, see Fig. (2(b)). To witness the entanglement,
we require ${\cal W}<0$ [29].

(a) Entanglement phase comparison for different sources.

(b) Entanglement witness value as a function of total decoherence $\Gamma$ for
various interferometer separation distances $d$.

Figure 2: Entanglement phase and witness values comparisons between different
signal sources as a function of the total decoherent $\Gamma$. Here each
interferometer is as shown in Figure 1(b), with $m=3.8\times 10^{-19}$ kg,
$T\approx 0.077$ s, $t_{p}\approx 160~{}\mu$s which gave the particles enough
time to complete one full period of oscillation in the $z$ direction.

Fig. 2(a) shows how the entanglement phase from each particle-particle differs
with regards to the separation between the two matter-wave interferometers for
both the external magnetic field-induced dipole-dipole entanglement and the
CP-induced entanglement. We can see that the entanglement witness due to the
magnetic dipole-dipole interaction dominates, as expected, at distances
$d>6{\rm\mu m}$, see Fig. 2(b). Below this CP-induced entanglement dominates,
as expected again due to the fall-off of the interaction strength with regard
to the separation distance $d$. In Fig. 2(b), we have taken the range of
decoherence rates and shown that the dominant entanglement is due to the
induced magnetic dipole-dipole interaction. Here we have assumed the mass is
similar in both the interferometers, $m=3.8\times 10^{-19}$kg, and the largest
superposition we are generating around $\sim 1.1{\rm\mu m}$.

Before we conclude, we should mention that the time duration of coherence for
the NV spin is one of the limiting factors, but the spin coherence times are
perpetually increasing (approaching 1s [40], even 30 s [41]), but adapting to
our scenario remains an open challenge [50]. We will also have to make sure
that the external temperature is below $1$k and the gas pressure is near
${\cal O}(10^{-15})$ Pa. In our analysis we have assumed that the NV spin is
not wobbling due to external torque, in reality, the NV spin will processes,
and future analysis has to be taken into account [51]. The nano-diamond can
also wobble in the presence of the external magnetic field [52]. However, this
can be suppressed even before being released from the trap, for example, by
using anisotropically shaped nanoparticles, which can be aligned with any
given direction in space by using linearly polarized lasers or electric fields
[53] or magnetic fields [54]. Besides, there will be vibrational excitations
from the breathing mode of the nano-diamond, e.g. phonon vibration, which we
will need to analyze for this experiment. The phonon vibration can be
suppressed for any state manipulation which does not excite the phonons in
resonance. We also note that it has already been shown that the internal
degrees of freedom (phonons) do not pose a problem [55].

To conclude, we have found a new entanglement for any matter-wave
interferometers, which relies on creating the macroscopic quantum
superposition with the help of a neutral diamagnetic nano-object in the
presence of an external magnetic field. Here we have shown for the first time
an explicit scheme to create a small-scale spatial superposition to test the
known electromagnetic-induced entanglements, the dominant effect arises from
external magnetic field-induced dipole-dipole entanglement which dominates for
the external magnetic field of ${\cal O}(1){\rm T}$, with a separation of
${\cal O}(10){\rm\mu m}$ for a mass of order $10^{-19}$kg.

As we have shown in Figs. 2(a),2(b), the entanglement is generated via the
external magnetic field induced in the nano-diamond, which is essential to
create the trapping potential and the superposition. The witness depends on
the total decoherence rate and the separation distance $d$. Such a system also
allows the characterization of what would be background effects in
gravitational mediated entanglement experiments. Indeed, we have shown how
optimizing the distance and trajectories can have a profound effect on the
various entangling interactions.

## Acknowledgements

R.J.M. is supported by the Australian Research Council (ARC) under the Centre
of Excellence for Quantum Computation and Communication Technology
(CE170100012). A.G. is supported in part by NSF grants PHY-2110524 and
PHY-2111544, the Heising-Simons Foundation, the John Templeton Foundation, the
W. M. Keck foundation, and ONR Grant N00014-18-1-2370. S.B. would like to
acknowledge EPSRC grants (EP/N031105/1, EP/S000267/1 and EP/X009467/1) and
grant ST/W006227/1.

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##  Appendix A Equations of Motion

A diamagnetic material in a magnetic trapping potential will evolve according
to the Hamiltonian

$\hat{H}=\frac{\hat{\bf{p}}^{2}}{2m}+\hbar
D\hat{S}_{z}+g_{s}\frac{e\hbar}{2m_{e}}\hat{\bf{S}}\cdot{\bf{B}}+mg\hat{y}-\frac{\chi_{\rho}m}{2\mu_{0}}{\bf{B}^{2}}$
(10)

where the first term in Eq.(10) represents the kinetic energy of the
nanodiamond, $\hat{\boldsymbol{p}}$ is the momentum operator and $m$ is the
mass of the nanodiamond. The second term represents the zero-field splitting
of the NV centre with $D=(2\pi)\times 2.8~{}{\rm GHz}$, $\hbar$ is the reduced
Planck constant and $\hat{S}_{z^{\prime}}$ is the spin component operator
aligned with the NV axis. The third term represents the interaction energy of
the NV electron spin magnetic moment with the magnetic field $\boldsymbol{B}$.
Spin magnetic moment operator
$\hat{\boldsymbol{\mu}}=-g_{s}\mu_{B}\hat{\boldsymbol{S}}$, where
$g_{s}\approx 2$ is the Landè g-factor, $\mu_{B}=e\hbar/2m_{e}$ is the Bohr
magneton and $\hat{\boldsymbol{S}}$ is the NV spin operator. The fourth term
is the gravitational potential energy, $g\approx 9.8$ ${\rm m/s^{2}}$ is the
gravitational acceleration and $\hat{\boldsymbol{z}}$ is the position operator
along the direction of gravity ($z$ axis). The final term represents the
magnetic energy of a diamagnetic material (diamond) in a magnetic field,
$\chi_{\rho}=-6.2\times 10^{-9}$ ${\rm m^{3}/kg}$ is the mass susceptibility
and $\mu_{0}$ is the vacuum permeability.

With this we can write the equations of motion as

$\displaystyle\partial^{2}_{t}{y}=$
$\displaystyle\frac{\chi_{\rho}}{2\mu_{0}}\partial_{y}{\bf{B}}^{2}-g_{s}\frac{e\hbar}{2mm_{e}}S_{y}\partial_{y}B_{y}-mg$
(11) $\displaystyle\partial^{2}_{t}{z}=$
$\displaystyle\frac{\chi_{\rho}}{2\mu_{0}}\partial_{y}{\bf{B}}^{2}-g_{s}\frac{e\hbar}{2mm_{e}}S_{z}\partial_{z}B_{z}-mg$
(12)

where we’re considering the motion in only 2 dimensions and the form of
${\bf{B}}$ is modified by the presence or absence of the pulsed magnetic
field. The total trajectory was then solved numerically and piece wise
depending on whether the pulsed magnetic field is present. The numeric
trajectory is shown with the potential energy due to the trapping potential is
shown in Figure 3

As a reminder, the magnetic field used for the trap is given by [47]

$\displaystyle{\bf{B}}_{T}=$
$\displaystyle-\left[\frac{3a_{4}\sqrt{\frac{35}{\pi}}x^{2}y}{8y_{0}^{3}}+\frac{3a_{4}\sqrt{\frac{35}{\pi}}y\left(x^{2}-y^{2}\right)}{16y_{0}^{3}}-\frac{a_{3}\sqrt{\frac{7}{6\pi}}x^{2}}{y_{0}^{2}}+\frac{a_{2}\sqrt{\frac{15}{\pi}}y}{4y_{0}}+\frac{a_{3}\sqrt{\frac{7}{6\pi}}\left(-x^{2}-y^{2}+4z^{2}\right)}{2y_{0}^{2}}\right]\hat{x}$
$\displaystyle-\left[-\frac{3a_{4}\sqrt{\frac{35}{\pi}}xy^{2}}{8y_{0}^{3}}+\frac{3a_{4}\sqrt{\frac{35}{\pi}}x\left(x^{2}-y^{2}\right)}{16y_{0}^{3}}-\frac{a_{3}\sqrt{\frac{7}{6\pi}}xy}{y_{0}^{2}}+\frac{a_{2}\sqrt{\frac{15}{\pi}}x}{4y_{0}}\right]\hat{y}-\left[\frac{2a_{3}\sqrt{\frac{14}{3\pi}}xz}{y_{0}^{2}}\right]\hat{z}$
(13)

where $y_{0}=75~{}\mu$m is the distance from the center of the trap to the
pole pieces which help generate the trap and $a_{2}=-1.3$ T, $a_{3}=0.0171$ T,
and $a_{4}=0.72$ T determine the magnetic field strength. The linear, pulsed
magnetic field used was

${\bf{B}}_{p}=\eta\left(y(t=0)-y\right)\hat{y}+\eta z\hat{z}$ (14)

where $\eta$ gives the magnetic field gradient and $y(t=0)$ is the initial
position of the particle in the $y$ direction, which is away from the minimum
of the potential for the particle. The potential energy as experienced by each
spin state during the pulsed magnetic field is shown in Figure 4.

Figure 3: Example interferometer trajectory superimposed on the potential
energy due to the combination of gravity and the trapping magnetic field in
the $y-z$ plane.  Figure 4: Potential energy for each spin state during
pulsed, linear magnetic field gradient. This is shown here in the starting
$x=0$, $y=-1.111$ $\mu$m plane, the pulsed magnetic field is switched off as
the particles reach the minimas at $z\approx\pm 0.1$ $\mu$m.


# A Short Overview of 6G V2X Communication Standards

###### Abstract

We are on the verge of a new age of linked autonomous cars with unheard-of
user experiences, dramatically improved air quality and road safety, extremely
varied transportation settings, and a plethora of cutting-edge apps. A
substantially improved Vehicle-to-Everything (V2X) communication network that
can simultaneously support massive hyper-fast, ultra-reliable, and low-latency
information exchange is necessary to achieve this ambitious goal. These needs
of the upcoming V2X are expected to be satisfied by the Sixth Generation (6G)
communication system. In this article, we start by introducing the history of
V2X communications by giving details on the current, developing, and future
developments. We compare the applications of communication technologies such
as Wi-Fi, LTE, 5G, and 6G. we focus on the new technologies for 6G V2X which
are brain-vehicle interface, blocked-based V2X, and Machine Learning (ML). To
achieve this, we provide a summary of the most recent ML developments in 6G
vehicle networks. we discuss the security challenges of 6G V2X. We address the
strengths, open challenges, development, and improving areas of further study
in this field.

###### Index Terms:

6G, V2X, AI, ML

Donglin Wang1, Yann Nana Nganso1, and Hans D. Schotten1

##  I Introduction

Vehicle-to-Everything (V2X) communications have the potential to drastically
reduce the number of vehicle collisions and as a result the number of deaths
[1]. In recent years, V2X communications have attracted significant research
interest from both academia and industry [2]. V2X communications consist of
Vehicle-to-Vehicle (V2V), Vehicle-to-Pedestrian (V2P), Vehicle-to-
Infrastructure (V2I), and Vehicle-to-Network (V2N) communications are examples
of V2X communications that increase road safety, traffic efficiency, and the
availability of infotainment services.[3].

The Federal Communications Commission (FCC) of the United States [4] allocated
75 MHz of spectrum in the 5.9 GHz band for Intelligent Transportation Services
(ITS) in 1999. This development enhanced significant research activity around
the technology of V2X communications. The results gave the first set of radio
channels for V2X completed in 2010 [4]. These standards, known as Dedicated
Short Range Communications (DSRC) are based on IEEE 802.11p technology.
Following the creation of radio standards, higher-layer standards, message
formats, protocols, and applications emerged [4]. The 3rd Generation
Partnership Project (3GPP) enables through Release 12 (Rel.12) the
availability of Device-to-Device (D2D) communications in Long Term Evolution
(LTE), therefore, allowing competitive broadband communication technology for
public safety networks [5]. According to [3] the achievement of better system
performance of V2X services and LTE-based V2V is due to Release 14 (Rel.14).
Rel.14 introduces LTE communication technology into vehicular networks
(denoted LTE-V2X). It functions in two modes: network-based mode, which uses
the LTE-Uu interface as the interface between a vehicle and a network
infrastructure, and direct mode, which is based on D2D communications defined
in 3GPP Release 13 (Rel.13), allowing devices to directly communicate (eg V2I,
V2P) through the PC5 interface, known as the LTE sidelink considering the
network infrastructure is not involved [6]. In 2018, the V2X 5G New Radio (5G
NR) technology was launched with the intention of enabling functions like
vehicle platooning, advanced driver assistance, and remote driving.
Furthermore, enhancements were made to the PC5 interface to increase its
reliability, reduce latency, and boost data rates through methods such as
carrier aggregation and advanced modulation techniques like 256QAM. Release 16
(Rel.16) is one of the few versions created by 3GPP on a cellular V2X based on
5G. It should be mentioned that Rel.16 seeks to deliver Ultra Reliable Low
Latency Communication (URLLC) and better throughput while also enhancing and
optimizing Rel.15 capabilities.

3GPP is actively developing Release 17 (Rel.17), which will include
architectural improvements to accommodate sophisticated V2X devices. URLLC is
only allowed to operate in the licensed spectrum in Rel.15 and Rel.16. Due to
the high demand for data transmission in 5G unlicensed spectrum becomes
helpful in the licensed spectrum which suffers from low-cost bandwidth. The
characteristics of the unlicensed spectrum do not take into consideration the
URLLC in Rel.15 and Rel.16. This is why Rel.17 was designed to unify the
characteristics of the unlicensed spectrum with URLLC, allowing URLLC to
function at the expected latency and dependability. [7]. In Fig. 1 we can see
the unlicensed evolution of 3GPP [8].

Figure 1: 3GPP unlicensed evolution

3GPP intends to improve the coverage of physical random access channels and
approaches to boost User Equipment (UE) power in Release 18 (Rel.18). In
addition, Rel.18 will introduce mechanisms to procedures for layer 1/layer2
based intercell mobility and will enable multi-SIM UE to indicate its
preferred capability restriction to network A when the UE needs to communicate
with network B. Furthermore, Rel.18 will study low-power wake-up receiver
architectures; this procedure will support the wake-up receiver and the
signal. It will also support 5G NR for devices onboard aerial aircrafts, such
as Unmanned Aerial Vehicles (UAVs). Fig. 2 shows the evolution of 3GPP
Releases [9]. The main contributions of this paper include the following:

  * •

Present the current and future development in V2X Communication.

  * •

Examine and contrast the main performance characteristics of current vehicle
technology with the anticipated needs for vehicular communication.

  * •

Describe the developments in V2X communication now and in the future.

  * •

Evaluate the security issues in V2X vehicular systems

This study is an attempt to suggest a description of the 6G V2X Communication
standards. The paper is organized as follows. Section II will include the most
current communication innovations connected to V2X. The use of 6G-V2x will be
explained in Section III. In Section IV, we will present the new technologies
for 6G V2X. Section V explains the security difficulties in V2X communication.

##  II Vehicle communication technologies

The communication technologies examined in this study are described in this
section.

###  II-A Dedicated Short-Range Communication

Vehicles and infrastructure are able to establish secure, swift, and direct
communication using DSRC, which is a wireless networking technology based on a
variation of WiFi. DSRC operates within the 5.85 to 5.925 GHz frequency band,
a dedicated spectrum reserved for vehicular communication with the Intelligent
Transportation System (ITS). [10].

###  II-B Long Term Evolution in 4G

LTE is a cellular communication network that was developed by the Third
Generation Partnership Project (3GPP) to address V2X communication concerns
[10]. Cellular V2X (C-V2X) was launched by 3GPP in 2016 with the combination
of LTE technology with vehicular communication [11].

Table I: Vehicular Communication Technologies and Key Performance Indicators Application requirements | 6G | 5G | 4G LTE | DSRC
---|---|---|---|---
Frequency | up to 1 THz | 3-300 GHz | 1.88-1.9 GHz | 5.85-5.925 GHz
Mobility | Up to 1000 km/h | Up to 500 km/h | Up to 140km/h | Up to 40 km/h
Satellite Integration | yes | No | No | No
Extreme Data Rate | 100 Gbps | 1Gbps | 100 Mbits/s | 27 Mb/s
Ultra-micro latency |  $<$1ms | 10ms |  $<$100ms | 150ms
Artificial Intelligence | Yes | No | No | No
Live Traffic | Yes | No | No | No
Big Data handling | Yes | No | No | No
Real-time hazard updates | Yes | No | No | No
Sharing HD 3 Dimension maps | Yes | No | No | No

###  II-C 5G

3GPP began the 5th generation mobile network, which focuses on the
digitization of industry and servicing customers. According to [12] 5G
enhances c-V2X communication with a capacity increase of 1000-fold, a data
throughput of 1 Gbps, ample bandwidth in densely populated areas, improved
responsiveness, decreased latency, and heightened reliability.

###  II-D 6G

Due to the inclusion of smart applications and modern technologies, vehicular
communication equipment is becoming more complex. When it comes to speed, 6G
surpasses 5G by a factor of 100. Additionally, 6G is considered the most
intelligent and efficient cellular network compared to its predecessors.
Consequently, 6G has been designed as the initial generation of cellular
networks to rectify the limitations of the 5G network.

##  III Why 6G-V2X?

For around two years, 5G in the frequency range 1 (FR1, or sub-6 GHz bands)
has been effectively implemented all over the world. However, because mmWave
access is limited to a smaller number of places, primarily in densely
populated areas, the Return on Investment (ROI) of millimeter-wave (mmWave) 5G
deployment in the frequency range 2 (FR2: 24-40 GHz) has just recently begun.
mmWave radio access is a very promising opportunity for operators and
manufacturers in the telecommunications sector to offer users new, enticing
services, not just for high-performance use cases but as a technology enabler
of smart cities supported by a knowledgeable ecosystem with robots, tactile
internet, Virtual and Augmented Reality (VAR), and pervasive ITS. Artificial
Intelligence (AI) at all levels is bracing these and other industries, along
with the expanding availability of reliable, safe, and enormously exploitable
data sources [13]. Given this perspective, it is possible that 5G NR-based V2X
networks will not be able to support all of the necessary specifications and
use cases. Furthermore, while the ideas behind ITS have been extensively
examined for many years, legacy V2X communication technologies can only offer
a certain amount of intelligence. As a result, a significant paradigm change
is required away from traditional communication networks and toward more
adaptive and diversified network strategies. This transformation is expected
to begin with the recently announced 6G wireless communication network, which
would incorporate a variety of non-terrestrial communication networks,
including satellite and UAV communication networks. As displayed in Table I,
the 6G-based V2X technology demonstrates a superior capability in addressing a
wide array of application requirements in comparison to its traditional V2X
communication counterparts. This advancement in 6G not only brings faster
speeds and lower latencies but also enhances the overall efficiency and
reliability of V2X communications, paving the way for more innovative
applications and improved user experiences in the realm of vehicular
communication.

With billions of connected communication devices, this will allow for truly
intelligent and ubiquitous V2X systems with greatly improved reliability and
security, extremely high data rates (such as Tbps), massive and hyper-fast
wireless access, and much smarter, longer, and greener (energy-efficient)
Three-Dimensional (3D) communication coverage.

Due to the very diverse composition of the network, variable communication
situations, and stringent service requirements, future V2X networks will
require unique approaches to facilitate adaptive learning and intelligent
decision-making. The combination of 6G with ML is expected to bring about
several new characteristics, including improved context awareness, self-
aggregation, adaptive coordination, self-configuration, and the full potential
of radio signals by evolving to intelligent and autonomous radios [2].

Figure 2: 3GPP’s 5G evolution roadmap

##  IV New technology for 6G-V2X

This section introduces some of the cutting-edge technologies that could be
used in 6G-V2X.

###  IV-A Brain-Vehicle Interfacing

Instead of a physical link between the driver and the vehicle, a Brain-
Controlled Vehicle (BCV) is driven by the driver’s thoughts. BCV may
considerably boost freedom for people with disabilities by providing them with
an additional interface for controlling automobiles. The brain-vehicle
interface has the potential to improve manual driving by anticipating a
driver’s actions and sensing discomfort. While the ultimate aim is fully
automated vehicles, managing the unpredictability and intricacies of
autonomous driving will necessitate human adaptability. A brain-vehicle
interface is expected to mitigate the challenges of autonomous driving in
challenging and uncertain situations, like rural and less organized areas, by
maintaining human involvement. While services connected to brain-machine
interactions would demand concurrent ultrahigh dependability, ultralow
latency, ultrahigh data rate connectivity, and ultrahigh-speed computing,
current wireless communications (e.g., 5G) and compute technologies are unable
to actualize BCV. For instance, a rough estimate of the full brain recording
requirement puts it at roughly 100 Gb/s, which present wireless technology
cannot handle. However, to assist learning and adapt to the behavior of human
drivers, 6G-V2X must use a fully phased brain-vehicle interface and ML
approaches.

###  IV-B UAV/Satellite-Assisted V2X

Due to their extensive aerial coverage, UAVs have the potential to act as
airborne wireless access points within the 6G-V2X network. These unmanned
aerial vehicles can offer various services to mobile customers, such as
relaying data, storage, and computational capabilities. UAVs can work together
with base stations and other components of the immobile network
infrastructure, especially in highly congested vehicle environments, to manage
the wireless network and improve the user experience. Unmanned Aerial Vehicles
(UAVs) offer numerous distinctive V2X applications as airborne agents,
benefiting from their nearly unrestricted three-dimensional mobility. These
applications include: 1) Offering early reports of road accidents prior to the
arrival of rescue teams. 2) Surveillance of traffic violations to support law
enforcement agencies; and 3) Disseminating warnings regarding road hazards in
regions lacking pre-installed Roadside Units (RSUs). Another possible airborne
communication vehicle for 6G-V2X communications is to use satellites.
Satellites are currently utilized in the V2X specifications for localization.
It is important to note that satellite transmission data rates have increased
significantly recently. Multibeam satellites, for example, have been widely
employed in satellite communication networks due to their ability to boost
wireless transmission throughput. As a result, 6G-V2X may use satellite
communication as a method to help contact between a car and a distant data
center in a situation where there is no terrestrial service. Similar to UAV-
based V2X communication, a satellite can also perform network and computing
tasks [2].

###  IV-C Integrated Control and Communication

A key component of 6G will be integrated communication and management, which
may also contribute to the advancement of sophisticated and autonomous V2X
services. One use of integrated communication and management is vehicle
platooning, in which a group of automobiles travels closely together in a car-
coordinated motion without any mechanical connection. The capacity of the road
is increased, fuel economy improves and pleasant road trips are three of the
main advantages of car platooning. To synchronize their acceleration and
slowdown, each vehicle in the platoon needs to know the relative distance and
velocity of its nearby vehicles [2].

###  IV-D Blocked-Based V2X

The wide adoption of V2X networks is highly dependent on authentication and
message propagation for large-scale vehicle traffic. This concept sets new
restrictions on how resources may be distributed in V2X networks. To combat
potential malicious assaults or jamming, mission-critical communications, for
instance, should have ultra-resilient security, but multimedia data services
may simply need lightweight protection owing to the volume of data. Different
frame structures, routing, power, and spectrum allocation techniques result
from these two different kinds of security needs. 6G-V2X might use a
blockchain system, which is considered a disruptive technology for safe
multiparty decentralized transactions. The utilization of blockchain
technology presents a range of enhanced security and privacy services,
distinct from traditional security solutions, as it eliminates the need for
intermediaries. Blockchain’s inherent distributed ledger technology enables
decentralized security management, offloading tasks to mobile cloud/edge/fog
computing, and caching content within 6G-V2X communication. In the context of
6G-V2X, a blockchain-based security solution, such as a smart contract or
consensus mechanism, is expected to not only verify message authenticity but
also safeguard the sender’s privacy. Blockchains also play a pivotal role in
managing unlicensed spectrum, enabling multiple users to share the same
spectrum. 6G-V2X may adopt a blockchain-based approach to spectrum sharing,
potentially delivering a more secure, intelligent, cost-effective, and highly
efficient decentralized spectrum-sharing solution. Although there have been
various attempts to implement a blockchain-based communication network, the
dynamic nature of the V2X communication situation and the need for real-time
data processing preclude a straightforward adoption of existing blockchain
technology. The technology itself suffers from excessive latency, despite
blockchain’s enormous promise to provide improved security and network
management. Consequently, the development of new blockchain algorithms with
ultra-low latency is imperative before their integration into 6G-V2X can be
realized. Some significant outstanding issues with existing blockchain
technology that require in-depth research include its limited throughput and
scalability.

###  IV-E Machine Learning

Recent developments in ML studies have allowed the development of new
technologies such as self-driving cars and speech assistants due to the
availability of large data sets, storage and computing capacity. Given this
context, ML has become more and more crucial to the highly independent and
clever functioning of tomorrow’s 6G vehicular networks. Traditional wireless
communication system design is heavily dependent on model-based methodologies,
in which different communication system building elements are carefully built
based on analysis of measurement data. Although these model-based methods have
proven effective in designing conventional communication systems, there may be
some 6G-V2X situations where precise modeling (such as an accurate
interference model and channel estimation) is unlikely.In the previously
mentioned scenarios, where traditional communication system design might
encounter discrepancies in model compatibility, ML proves to be a potent
instrument due to its ability to discern features and detect relationships,
even those concealed deeply, between input and output data. Furthermore, the
data-driven essence of machine learning can facilitate predictions and
projections regarding user behavior, network traffic, application needs,
security threats, and channel dynamics. This, in turn, leads to improved
resource allocation and enhanced network performance. Recent advancements in
machine learning (ML) methods are significantly contributing to the progress
of autonomous vehicles, while also playing a crucial role in enhancing the
overall driving experience and road safety. Take, for instance, the wealth of
data streams originating from sources like cameras, Light Detection and
Ranging (LiDAR) sensors, GPS units, and various sensors. These data streams
can be efficiently processed, allowing for the application of modular
perception, planning, action, or end-to-end learning techniques in automated
driving, enabling data-informed intelligent decision-making. In the realm of
ML-based vision, there’s ongoing exploration of multimodal reasoning. This
involves the integration of camera frames and LiDAR scans to enhance object
detection, a vital element in automated driving safety.Our focus in this paper
is on the network perspective, highlighting the influence of ML within 6G-V2X
networks. However, it’s worth noting that numerous ML-driven applications for
intelligent driving are anticipated in the future. We also introduce one of
the most cutting-edge ML techniques, federated learning [2].

####  IV-E1 ML for security management

The merge of various forms of communication and the strict data delivery
requirements for 6G-V2X will worsen security problems.The inherent broadcast
nature of vehicular communication exposes it to potential security
vulnerabilities and malicious attacks, although 6G-V2X seeks to provide smooth
access between infrastructure sites and cars. A vehicular network could be the
subject of numerous malicious attacks, including approved and sanctioned
attacks, data forgeries, and distributions [14]. A new user identification and
verification method must be developed to maintain safe and legal access to
data, services, and systems because private user information, such as user
identity or trajectory, is shared over wireless links in a V2X system [15]. In
[16] and [17], supervised learning with categorization capacity is suggested
as a useful tool to detect abnormal driving behavior in cars. It is stated
that because training and detection processes rely on previously labeled data,
supervised learning may not be able to identify new or undiscovered assaults.
Unsupervised learning, which can aggregate data without the need for labeled
information, is being considered for real-time recognition in [18] and [19].
For vehicle networks, intruder detection using K-means clustering is
specifically suggested in [18]. Anomaly detection using unsupervised learning
is researched in [19] to combat assaults that can occur spontaneously in real-
time. Nonetheless, these approaches exclusively focus on either misuse
detection or anomaly detection, which may not effectively address real-world
scenarios where both known and undiscovered attacks could occur
simultaneously. Additionally, to reduce transmission costs, reactive detection
is taken into account primarily in current detection methods.Nonetheless, it
is anticipated that proactive exploration-based security methods will be
beneficial for elevating the security standards within a 6G-V2X network,
particularly in scenarios where communication resources are relatively
abundant [20]. For example, [21] adopts a proactive anomaly detection strategy
for linked vehicles to avoid cyber threats. Typically, cryptographic
techniques are used in the higher layers of the protocol stack to handle
security problems in wireless transmission. However, in diverse and dynamic
V2X networks where cars may haphazardly enter or exit the network at any
moment, the administration and exchange of private keys will be difficult
[22]. In this sense, Physical Layer Security (PLS) solutions can be used to
complement conventional encryption methods [23]. While Physical Layer Security
(PLS) techniques leverage the physical attributes and stochastic behavior of
wireless channels to mitigate eavesdropping, they can still be influenced by
the accuracy of channel modeling. In a V2X context marked by high mobility and
frequent channel variations, the use of machine learning becomes advantageous
for accurate channel prediction and monitoring. This, in turn, has the
potential to enhance the effectiveness of PLS-based methods. Furthermore,
various security levels are anticipated according to the situations and
services. Consider, for instance, two cars that track one another either at a
busy junction or on a deserted road. Due to the mobility of cars, the latter
has a greater number of variables that can influence decision-making, leading
to strict security requirements [24]. In the latter scenario, ML may be used
to dynamically determine the necessary security degree and the best PLS
answer. As demonstrated in [25], ML can also play a role in enhancing the
management and communication systems designed to safeguard against data
injection attacks within specific vehicle platoons. When ML is used to improve
security, the end-to-end network efficiency of the ML-based system must be
validated. As stated above, ML can be applied to functional components at
various network levels. To ensure that all interactions are secure, ML usage
should be coordinated across the network [26].

####  IV-E2 Federated Learning for 6G-V2X

Training ML models, which can be used at base sites or in vehicles, is a key
problem for effective use of ML. Training a large ML model in distant clouds
is an apparent answer, but it may take some time. One issue is that a sluggish
reaction to external changes could result from rapidly changing vehicle
network and communication conditions, which would affect performance.
Furthermore, given that the majority of training data is generated at network
edges, such as base stations and mobile vehicles, the expense and latency
associated with transmitting this data to a remote cloud can be substantial.
In view of this, conducting local training of machine learning models within
6G-V2X networks emerges as a more favorable choice. To increase the accuracy
and generalization of the performance of ML models, joint training samples are
a possible solution. This is because each base station or car may only be able
to store a limited number of training samples.While base stations and vehicles
may have concerns about compromising their privacy by sharing training data,
privacy remains a significant concern in collaborative training. Federated
learning, a relatively recent approach designed to address privacy and
transmission overhead issues associated with ML model development, has
garnered considerable research attention as a means to enhance wireless
networks. [27] [28] [29] [30]. There are numerous technological challenges to
address when implementing federated learning applications, which are regarded
as a promising machine learning approach for enhancing the efficiency of
6G-V2X networks. Supervised learning is taken into account primarily in the
study that has already been conducted on shared learning in wireless networks.
As the use of Reinforcement Learning (RL) models increases, a flexible
federated RL system is required that can accommodate a variety of 6G-V2X use
cases. Furthermore, initiating federated RL (reinforcement learning) from a
blank slate is often infeasible since many V2X applications are mission-
critical, and such an approach could lead to an unstable initial phase during
the learning process. The limited connection between vehicles presents another
difficulty for federated learning involving cars. Vehicles may not be in
contact with base units or other federated learning-related vehicles.
Therefore, while they are stopped, the cars might need to participate in
federated learning. Lastly, a more comprehensive study is needed to determine
how the wireless route affects the effectiveness of federated learning.
Wireless delays and errors can affect the precision of federated learning, as
demonstrated in [28]. The high-speed mobility of vehicles and the dynamic
nature of channels within a mobile V2X network could exacerbate this effect.
Further research is essential to explore the integrated development of
wireless and learning processes for V2X applications.

##  V V2X communication security

When it comes to communication across public or private networks, one of the
primary issues is security. When transmitting, receiving, and processing
sensitive data over networks, network systems are susceptible to a range of
threats, including denial of service attacks, eavesdropping, and challenges
related to digital identity verification. V2X technology enables vehicles to
autonomously detect and respond to rapidly changing objects as symbols. If the
information exchanged within the vehicular network is accessed and modified
without authorization, it could lead to catastrophic consequences for the
vehicle’s decision-making process. As an illustration, within an autonomous
vehicle, remote control over components like the steering wheel and braking
system is possible. If an unauthorized party gains control over these
functions, it could lead to potential harm to both property and individuals.
Furthermore, one of the most well-known ideas today that makes it easier to
manage city traffic is the Intelligent Transport System. Among the most
important traffic management practices are the enhancement of traffic flow
through analysis of daily traffic patterns, traffic prioritization, and upkeep
of intelligent traffic signals. The security of the community and the
Intelligent Transportation System (ITS) is jeopardized when unauthorized
individuals gain access to the data, and the entire network could be disrupted
if any data is compromised or tampered with.

##  VI Conclusion

In this article, we identified several enabling technologies for 6G V2X
communications. Our main focus was to understand how 6G-V2X functions and its
applications. 6G technology excels in meeting the requirements for V2X
communication. Nevertheless, security remains a significant challenge in V2X
communication and must be effectively addressed to drive further advancements
in 6G technology.d We hope that this article with provide specific details in
6G-based next-generation V2X for other scientists and engineers which will
also encourage more research and solutions on this topic.

##  VII acknowledgement

This work has been supported by the Federal Ministry of Education and Research
of the Federal Republic of Germany (BMBF) as part of the Open6GHub project
with funding number 16KISK004. The authors would like to appreciate the
contributions of all Open6GHub partners. The authors alone are responsible for
the content of the paper which does not necessarily represent the project.

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