# Automated distribution of high-rate, high-fidelity polarization entangled
photons using deployed metropolitan fibers

Alexander N. Craddock  Anne Lazenby  Gabriel Bello Portmann  Rourke Sekelsky
Mael Flament  Mehdi Namazi  Corresponding author<EMAIL_ADDRESS>Qunnect
Inc., 141 Flushing Ave, Ste 1110, Brooklyn, NY 11205-1005

###### Abstract

Distributing high-fidelity, high-rate entanglement over telecommunication
infrastructure is one of the main paths towards large-scale quantum networks,
enabling applications such as quantum encryption and network protection, blind
quantum computing, distributed quantum computing, and distributed quantum
sensing. However, the fragile nature of entangled photons operating in real-
world fiber infrastructure has historically limited continuous operation of
such networks. Here, we present a fully automated system capable of
distributing polarization entangled photons over a 34 km deployed fiber in New
York City. We achieve end-to-end pair rates of nearly $5\times 10^{5}$ pairs/s
and entanglement fidelity of approximately $99\%$. Separately, we achieve 15
days of continuous distribution, with a network up-time of $99.84\%$. Our work
paves the way for practical deployment of 24/7 entanglement-based networks
with rates and fidelity adequate for many current and future use-cases.

##  I Introduction

Entangled photons not only enhance the current capabilities of quantum links
for applications in secure communication [1, 2], they are also fundamental for
building large scale quantum repeaters [3], distributed quantum computing [4,
5, 6, 7], and distributed quantum sensing networks [8, 9, 10]. All such use-
cases rely on access to high-rate, high-fidelity entanglement across the
network. Therefore, the high-performance distribution of entanglement over
quantum channels is essential for any future quantum network.

Given their weak environmental interactions and speed of propagation, photons
are a natural choice as communication qubits. Among different types of
photonic qubits, polarization states provide many advantages such as ease of
creation, manipulation, and measurement. Such states are also prime candidates
for interfacing with atomic and ionic systems [11, 12, 13], paving the way
towards larger scale distributed quantum networks.

Owing to the large amount of unused fiber available and the manageable optical
losses over short ranges, telecom fibers are a good choice for photonic
quantum channels in metropolitan areas. However, environmental factors can
readily affect fibers and cause changes to the polarization, typically
represented as rotations in the Poincaré sphere [14]. These can be both
wavelength and time-dependent, and can in turn degrade fiber performance as a
quantum channel for entanglement distribution. As a result, compared to other
type of entanglement networks [15, 16], the demonstrations of high-fidelity
polarization qubit distribution over extended periods of time are difficult
[17]. However, due to the advantageous properties of these qubits, much
research has been performed on their distribution. In the past two decades the
field has improved from the early stage experiments over approximately $1$ km
fibers [18] to inter-country [17, 19] and high rate [20] links.

Presently, much of the literature has focused on proof-of-principle
experiments. However, practical entanglement networks will require stable,
long-term useable polarization entanglement distribution with high-rate, high-
fidelity, and high network up-time. Here, we report a series of measurements
performed through buried fiber optics in New York City, using Qunnect’s
GothamQ testbed shown in Fig. 1. We characterize the polarization dispersion
properties of the fibers in the GothamQ testbed. Then, using a narrow-band
polarization entanglement source and an active polarization-compensating
device, we demonstrate entanglement distribution with throughputs of nearly
$5\times 10^{5}$ pairs/s and fidelities of approximately $99\%$ over a 34 km
long fiber with a total loss of 17.4 dB. We show that the entanglement
distribution system is capable of operating with high performance for over
$15$ days without any user input, maintaining a network up-time of $99.84\%$.
To the best of our knowledge, these experiments are the first showcase of
practical and fully automated distribution of entangled photons at high rates
and fidelity, enabling a wide range of applications.

Figure 1: Experimental setup for entanglement distribution experiments.
Background shows the path of the GothamQ fibers. Upper left (lower right)
diagram shows the experimental apparatus prior to photons entering (exiting)
the GothamQ fiber. PBS: polarizing beam splitter, DM: dichroic mirror, BPF:
bandpass filter, LCR: liquid crystal retarder, HWP: half waveplate, L: Lens,
LP: Linear Polarizer, AOM: acouto-optic modulator, FPC: Fiber polarization
compensator, OS: Optical switch, SPAD: Single photon avalanche detector,
SNSPD: Superconducting nanowire single photon detector.

##  II Fiber Polarization Dispersion

Figure 2: “Instantaneous” fiber polarization dispersion measurements. For each
plot the legend indicates the number of GothamQ fibers used for the
measurement. a) displays the Poincaré sphere rotation as a function of
wavelength relative to the input. b) shows the Poincare sphere rotation
relative to the average rotation value as a function of wavelength. c)
displays the Poincaré sphere rotation between two wavelengths a nanometer
apart. d) shows the expected fidelity for a narrowband Bell state where one
qubit is passed through the fiber, assuming at the exit of the fiber
configuration we have performed an operation to undo the Poincaré sphere
rotation for photons at $1300$ nm. e) shows the expected fidelity for a Bell
state where one photon, with center wavelength of $1300$ nm, is passed through
the fiber configuration as a function of the spectral width of the biphoton
pair. f) displays the expected fidelity for a Bell state for a biphoton pair
with a spectral FWHM of $10$ nm, as a function of center wavelength of the
photon passed through the fiber. In plots a) - d) line is provided to guide
the eye. Figure 3: Expected fidelity of a narrowband Bell state over time as a
function of the wavelength of the photon passed through one of the GothamQ
fibers. In each case the fidelity is calculated relative to the initial
Poincaré state of the fiber for each wavelength.

First, we characterize the polarization dispersion of the fibers in the
GothamQ network. For this work, we use a narrow linewidth laser (Thorlabs
TLX3) with a tunable range which covers nearly the entire telecom O-band. For
a given wavelength we generate three polarization states,
$\left\\{\ket{H},\ket{D},\ket{R}\right\\}$. We pass these through some fiber
configuration, and measure the resulting polarization states using a
polarimeter (Thorlabs PAX1000IR2).

First we assess the “instantaneous” polarization dispersion behavior. For each
of the three input polarizations, we sweep the wavelength of the tunable laser
from $1260$ nm to $1350$ nm with a $1$ nm step, recording the polarization
state at each wavelength. We perform this measurement for $0$ 111This
configuration does not pass through GothamQ, but the light traverses
approximately $20$ meters of fiber between common between all the other
measurements, $1$, $2$, and $3$ fibers within GothamQ in series (or distances
of $\approx 0$, $34$ $68$, and $102$ km respectively). We note that although
the measurement is not truly instantaneous, we have verified that in each case
the fiber was stable enough that this approximates an instantaneous
measurement. Knowing the output and input states, we calculate the Poincaré
sphere rotation that the fiber configuration performs (see supplementary). As
seen in Fig. 2a) and b), in all cases we observe some level of dispersive
polarization behavior. To better quantify the dispersion, we calculate the
Poincaré sphere rotation per unit nanometer, shown in Fig. 2c). From this, we
can see clearly that all the configurations which pass through GothamQ fibers
exhibit a much higher level of polarization dispersion than the configuration
which doesn’t.

Given the above fiber behavior, we are able to make some inferences about the
suitability of the fibers as quantum channels for distributing quantum
entanglement. In Fig. 2d), we calculate the fidelity for retaining a Bell
state when one qubit is transmitted across a given fiber configuration,
assuming we have performed the appropriate correction on the receiving end to
account for the Poincaré sphere rotation at $1300$ nm. By weighting curves
such as those in Fig. 2d) by a Gaussian with a given full-width half-max
(FWHM), we are able to make inferences about the fidelity of photon pairs
where one photon is propagated along the GothamQ fibers. In Fig. 2e) we show
the expected fidelity as a function of spectral FWHM of the biphoton pair
where the propagating photon has a center wavelength of $1300$, and in Fig.
2f) we display the expected fidelity as a function of central wavelength of
the propagated photon for a biphoton pair with a $10$ nm FWHM. We see that in
all configurations, increasing the pulse bandwidth decreases the expected
fidelity of the entangled state.

In addition to the “instantaneous” measurements, we measure the long-term
fiber polarization dispersion behavior, shown in Fig. 3. For the figure, we
calculate the change in fidelity of a hypothetical narrowband Bell state,
where one photon is passed through the GothamQ fiber, as a function of
wavelength.

From the data it is clear that high fidelity distribution of polarization
qubits necessitates that the photons used be narrowband. Given that some level
of polarization drift is observed for every wavelength measured in Fig. 3,
maintaining high fidelity polarization qubit transmission in an optical fiber
is likely to require active compensation. However, given our observations in
Fig. 2 and 3 such compensation needs to be done on the same fiber at the same
wavelength as the qubits.

##  III Entanglement Distribution

###  III.1 Experimental Setup

Next, we demonstrate entanglement distribution for pairs of photons where one
is distributed in a buried fiber within New York City. The experimental setup
for this is shown in Fig. 1.

We use a spontaneous four-wave mixing (SFWM) source based on warm atomic
vapors to generate entangled bichromatic photon pairs. In the source, a $780$
nm pump and $1367$ nm coupling beam excite atoms within an enriched
rubidium-87 vapor cell to the $\ket{6S_{1/2}}$ state via the $\ket{5P_{3/2}}$
intermediate state. From the doubly-excited state, emission of a $1324$ nm
photon may occur, projecting a collective $\ket{5P_{1/2}}$ excitation onto the
vapor [22]. Subsequent decay of this collective excitation, which is highly
directional, results in a photon at $795$ nm. Due to the Zeeman structure of
rubidium, and the co-linear pump and coupling polarization, the $1324-795$
pairs are emitted in a polarization entangled
$\ket{\Phi_{+}}=\frac{1}{\sqrt{2}}\left(\ket{HH}+\ket{VV}\right)$ Bell state
[23]. For these experiments we use a source setup similar to the one described
in [24]. Additionally, we use the optimal values for the pump and coupling
detunings, as well as the vapor cell temperature determined in [24].
Throughout the following, the pump and coupling powers are set to be equal,
and adjusted to achieve the different pair rates shown. An advantage of this
source is that it natively produces narrowband (linewidth less than $1$ GHz)
polarization entangled biphotons. From Fig. 2, this should mean the fidelity
of the entangled state after propagation should not be bounded by the photon
linewidth.

To preserve the fidelity of the entangled state as photons are passed through
the metropolitan fiber, we use our automated polarization compensation (APC)
devices. The APC operates as a pair, with an injector and a compensator at
either ends of the fiber. The APC injector produces a sequence of classical
pulses with well-defined polarization, created using a polarizer followed by
an elasto-electro-optic modulator (EEOM). We pass the classical pulses down
the fiber to be stabilized to the APC compensator. The compensator contains an
EEOM (with a modulation bandwidth of approximately $120$ kHz) and a fast
polarimeter ($10^{4}$ measurements/s). We initalize the pair by taking a
reference measurement with the polarimeter. After which, the compensator
adjusts its EEOM to ensure subsequent pulse sets from the injector match the
reference. We use time-division multiplexing to mix the classical pulse
sequence with light passed to the input port of the injector, via a set of
optical switches. For all the measurements shown, we trigger the APC
compensation cycle approximately every $20$ seconds. In each compensation
cycle, the fidelity is first measured by comparing the current state of the
fiber to the reference. If it is found to exceed a trigger threshold, (set
here to be $99\%$) then the compensation cycle finishes. If it is below the
threshold, we utilize a gradient descent algorithm to adjust the compensator
EEOM until it exceeds an optimization threshold (also set here to be $99\%$).
The compensation cycle takes between $30$ to $1000$ ms, depending on the
polarization rotation that has occurred on the fiber.

For this experiment, we couple the $1324$-nm telecom photons produced by the
source into a fiber attached to the input port of the APC injector which is in
turn connected to the buried $34$-km long metropolitan fiber, shown in Fig 1.
After travelling through the metropolitan fiber, we pass the telecom photons
to a fiber switch. From the switch we either pass the photons to the APC
compensator, or a fiber path which bypasses the compensator completely. A
further switch recombines the paths and sends the photons for polarization
analysis. With both switches we are able to toggle between compensating and
not compensating for drifts in the metropolitan fiber.

For analysis of the entangled state after fiber transit, we use a measurement
station for each of the two source photon wavelengths. In both cases, the
measurement station consists of a half-waveplate and a polarizing
beamsplitter. We perform polarization measurements for the $795$-nm photons
prior to fiber coupling at the source setup. For the $1324$-nm photons, we use
an independent measurement station setup that includes a bandpass filter. This
helps to minimize noise that may have been accumulated in the metropolitan
fiber. While full two-photon tomography requires both a quarter- and half-
waveplate for both photons for polarization analysis [25], we use a method
(see supplementary material) that allows us to bound the entangled state
fidelity using only measurements of the coincidences in the
$\left\\{\ket{HH},\ket{HV},\ket{VH},\ket{VV},\ket{DD},\ket{DA},\ket{AD},\ket{AA}\right\\}$
modes.

As discussed earlier, close matching of the wavelength of the classical and
quantum light is required to ensure good polarization compensation of the
fiber for the quantum light. Therefore, we use a $1324$-nm laser source as our
classical light for the APC injector, verified with a wavemeter to be within a
nanometer of the signal photons produced by the source. The laser is left free
running throughout the experiment. After coupling the classical light into
fiber, we pass the light through a fiber-based acousto-optic modulator (AOM).
The AOM is on/off controlled by the APC injector to shutter the classical
light when active compensation is not occurring. Along with the in-built
optical switches, this minimizes the noise present at the telecom measurement
station due to the APC. After the AOM, we use an in-fiber polarizer to ensure
a well-defined input polarization for the classical field passed to the APC
injector.

For the $1324$-nm photons, we use a pair of polarization controllers: one
prior to the APC injector input and one on the uncompensated path between the
two fiber switches. The initial polarization rotation performed by the
metropolitan fiber, as well as other shorter fibers within the setup, is
unknown. We use the fiber polarization controllers, along with a liquid
crystal retarder (LCR) on the source setup to undo this initial rotation for
the compensated and uncompensated paths. For the two experiments presented
later, the LCR and controllers were calibrated prior to any data being taken,
and then the values fixed for the duration of the experiment.

We detect the $795$-nm photons using a set of single-photon avalanche
photodiodes and the $1324$-nm photons using a superconducting nanowire single-
photon detector (SNSPD) ($\approx 350$-ps and $\approx 90$-ps timing jitters,
and $68\%$ and $90\%$ detection efficiencies, respectively). We find that the
metropolitan fiber has a loss of $14.45$ dB. Along with the other losses due
to other elements (see supplementary material), the total loss from the source
to the input of the telecom measurement station is $17.46$ dB.

###  III.2 Rate vs. Fidelity

Figure 4: Fidelity to the $\ket{\phi_{+}}=\frac{\ket{HH}+\ket{VV}}{\sqrt{2}}$
Bell state as a function of the throughput pair rate (after $1324$-nm photons
are passed through a single GothamQ fiber). For each pair rate an hour-long
dataset was taken. Inset is zoom in of the low rate behavior. Fidelity bounds
(see supplementary) are the mean over the dataset, error bars are from
statistical uncertaities. Theoretical fidelity is calculated as
$1-\frac{3}{2(1+g_{SI}})$ (see supplementary for derivation).

Here, we explore the dependence of the entanglement fidelity on the fiber pair
throughput. For this experiment, we adjust the pump and coupling powers to
change the source entangled pair generation rate. Given the probabilistic
nature of the entangled pair source used, we expect the pair cross-
correlation, and therefore the entangled state fidelity, to decrease as the
pair generation rate is increased (see supplementary). At each generation
rate, we take the fidelity-bounding measurements (described above)
approximately every four minutes for a total of four hours. For each fidelity-
bounding measurement we calculate the highest lower bound and the lowest upper
bound (see supplementary) on the fidelity to the
$\ket{\phi_{+}}=\frac{\ket{HH}+\ket{VV}}{\sqrt{2}}$ Bell state.

The average and standard deviation on the lower bounds over the four-hour
measurement duration are shown in Fig. 4 for various entangled pair rates. We
note that we can only bound the fidelity due to the measurement method chosen,
and that the bounds do not arise purely from experimental uncertainties (see
supplementary). At maximum pump and control power available for this
experiment, we can achieve an end-to-end pair distribution rates of
approximately $5\times 10^{5}$. At this throughput we’ve experimentally
bounded the entangled state fidelity to be $>0.84$. However, we believe the
state fidelity should be source limited to approximately $0.88$.

Reaching such high rates at a high fidelity over real life metropolitan
networks opens the path for practical deployment of entanglement-based
quantum-secured communication links. High fidelity distribution of entangled
photons is a key step towards networked quantum computing and distributed
quantum sensing over deployed fibers. While for high pair generation rates the
limit on the fidelity is from the source itself, at lower throughput rates,
around $2\times 10^{4}$ pairs/s, we can reach a fidelity of approximately
$0.99$, which is consistent with the thresholds set for the APC process.
Achieving such high fidelity for polarization entanglement distribution not
only surpasses all previous polarization based deployments, to the best of our
knowledge, it is on par with the state-of-the-art for time-bin and time-energy
based entanglement networks [15, 16].

###  III.3 Long-term usability measurement

Figure 5: Results of long-term usability measurement. a) shows the pair rate
observed through the compensated path. b) shows fidelity bounds (see
supplementary) for the compensated and uncompensated paths. c) shows the
uptime (time entangled pairs are being actively distributed). In both plots we
have performed a three-hour trailing average for ease of viewing. The
uncertainties quoted come from the statistical deviation within the three hour
averaging windows.

Another important aspect of a practical quantum network is the long-term,
uninterrupted distribution of photon pairs without the need for manual
intervention. Previous works [17] have shown great progress towards this goal
but still required relatively time-consuming manual or automatic optimizations
which in turn affected the overall network up-time. Here, we demonstrate the
long term usability of the entangled pairs when the $1324$-nm photons from the
source are transmitted over the $34$-km metropolitan fiber. For this
experiment the pump and coupling powers is fixed to produce approximately
$2\times 10^{5}$ pairs/s after passing through fiber. Our experimental loop
consists of taking fidelity bounding measurements both for a path compensated
by the APC, and an uncompensated path for comparison. The experimental cycle
is repeated approximately every four for over fifteen days. Similar to the
previous experiment, we calculate the highest lower and lowest upper bound on
the fidelity of the state, in both the compensated and uncompensated case, to
the $\ket{\phi_{+}}=\frac{\ket{HH}+\ket{VV}}{\sqrt{2}}$ Bell state.

In Fig. 5a) we show the entangled pair rate that passed through the
metropolitan fiber. The pair rate has been calculated by summing the number of
coincidences observed in the
$\left\\{\ket{HH},\ket{VV},\ket{HV},\ket{VH}\right\\}$ modes and dividing out
peak detection efficiencies. The observed downward trend in the pair rate over
the measurement period was recovered upon completion by adjusting the
polarization being sent to the SNSPD. Therefore, we believe that the actual
pair rate was stable over the course of the measurement.

As seen in Fig. 5b), the state fidelity for the path compensated by the APC is
approximately constant over the fifteen-day measurement, with average lower
and upper bounds of $0.937(7)$ and $0.967(4)$, respectively. Similar to
before, we believe at these rates the fidelity should be limited by the source
to approximately $95\%$. In contrast, the path which is uncompensated
experiences significant fluctuations over the course of the measurement, with
slow drifts observed in addition to discrete jumps.

In Fig. 5c) we show the uptime for the data run. We see that the above results
are achieved with a network uptime consistently above $99\%$, with a total
uptime of $99.84\%$ over the 15-day run. To the best of our knowledge, these
results are the first ever demonstration of highly stable distribution of
high-rate, high-fidelity polarization entangled photons under real-world
conditions, opening the path for 24/7 use of quantum entanglement within
telecommunication infrastructure.

##  IV Conclusion

The robust distribution of entanglement with high-rate and fidelity across
deployed fibers will be critical for the development of the quantum internet.
Here we presented data from a quantum test-bed in New York City, GothamQ,
demonstrating progress towards a fully automated, practical entanglement
network. Using 34 km of deployed fiber in the city, we showcased the
possibility to distribute polarization entangled photons with fidelity up to
$99\%$ and rates as high as $5\times 10^{5}$ pairs/s. Additionally, we
presented the long-term usability of the network, achieving high network up-
time ($>99.5\%$) for an extended period of operation ($15$ days). This
demonstration shows that robust, high uptime, round-the-clock operation of
entanglement distribution networks is attainable for practical use cases.

##  V Acknowledgments

We thank Thorlabs for generously lending us a TLX3 to perform the fiber
polarization dispersion measurements. We thank the Qunnect Inc. team,
especially Noel Goddard, Yang Wang, and Felipe Giraldo for their insights and
help with manuscript preparation.

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## Supplementary

##  VI Fidelity Bounding

Here, we derive a method of bounding the fidelity for a Bell state, given a
set of two-photon tomographic measurements in the linear polarization basis.
We consider a general two-photon density matrix

$\hat{\rho}=\begin{pmatrix}\rho_{11}&\rho_{12}&\rho_{13}&\rho_{14}\\\
\rho_{21}&\rho_{22}&\rho_{23}&\rho_{24}\\\
\rho_{31}&\rho_{32}&\rho_{33}&\rho_{34}\\\
\rho_{41}&\rho_{42}&\rho_{43}&\rho_{44}\end{pmatrix},$ (S1)

which has a fidelity to the
$\ket{\phi_{+}}=\frac{\ket{HH}+\ket{VV}}{\sqrt{2}}$ Bell state

$F=\left(\text{Tr}\left[\ket{\phi_{+}}\bra{\phi_{+}}\hat{\rho}\ket{\phi_{+}}\bra{\phi_{+}}\right]\right)^{2}=\frac{\rho_{11}+\rho_{44}+\rho_{41}+\rho_{14}}{2}.$
(S2)

We define a normalization factor

$N=C_{\ket{HH}}+C_{\ket{HV}}+C_{\ket{VH}}+C_{\ket{VV}},$ (S3)

where $C_{\ket{ij}}$ are the coincidences experimentally recorded between the
labelled polarization modes. For the
$\left\\{\ket{HH},\ket{HV},\ket{VH},\ket{VV}\right\\}$ basis we can write the
on-diagonal elements as

$\begin{split}\rho_{11}&=\frac{C_{\ket{HH}}}{N}\\\
\rho_{44}&=\frac{C_{\ket{VV}}}{N}.\end{split}$ (S4)

For the off-diagonal elements, we can make use of the Cauchy-Schwartz
inequality

$\left|\rho_{ij}\right|^{2}\leq\rho_{ii}\rho_{jj},$ (S5)

to write

$-2\sqrt{\rho_{11}\rho_{44}}\leq\rho_{14}+\rho_{41}\leq
2\sqrt{\rho_{11}\rho_{44}},$ (S6)

which allows us to bound the fidelity

$\frac{C_{\ket{HH}}+C_{\ket{VV}}-\sqrt{C_{\ket{HH}}C_{\ket{VV}}}}{N}\leq
F\leq\frac{C_{\ket{HH}}+C_{\ket{VV}}+\sqrt{C_{\ket{HH}}C_{\ket{VV}}}}{N}.$
(S7)

An additional bound can be found by noting that

$\frac{C_{\ket{DD}}+C_{\ket{AA}}}{N}=\frac{1+\rho_{14}+\rho_{23}+\rho_{32}+\rho_{41}}{2}.$
(S8)

Similar to equation S6, we can write

$-2\sqrt{\rho_{22}\rho_{33}}\leq\rho_{23}+\rho_{32}\leq
2\sqrt{\rho_{22}\rho_{33}},$ (S9)

and similar to the way we wrote the on-diagonal elements in equation S4 we can
write a further set of bounds for the fidelity

$\displaystyle F\geq$
$\displaystyle\frac{C_{\ket{HH}}+C_{\ket{VV}}+C_{\ket{DD}}+C_{\ket{AA}}-C_{\ket{DA}}-C_{\ket{AD}}-2\sqrt{C_{\ket{HV}}C_{\ket{VH}}}}{2N}$
(S10) $\displaystyle F\leq$
$\displaystyle\frac{C_{\ket{HH}}+C_{\ket{VV}}+C_{\ket{DD}}+C_{\ket{AA}}-C_{\ket{DA}}-C_{\ket{AD}}+2\sqrt{C_{\ket{HV}}C_{\ket{VH}}}}{2N}.$
(S11)

Due to the rotational symmetry of the Bell state, we can additionally write
bounds

$\frac{C_{\ket{DD}}+C_{\ket{AA}}-\sqrt{C_{\ket{DD}}C_{\ket{AA}}}}{N}\leq
F\leq\frac{C_{\ket{DD}}+C_{\ket{AA}}+\sqrt{C_{\ket{DD}}C_{\ket{AA}}}}{N}$
(S12) $\displaystyle F\geq$
$\displaystyle\frac{C_{\ket{DD}}+C_{\ket{AA}}+C_{\ket{HH}}+C_{\ket{VV}}-C_{\ket{HV}}-C_{\ket{VH}}-2\sqrt{C_{\ket{DA}}C_{\ket{AD}}}}{2N}$
(S13) $\displaystyle F\leq$
$\displaystyle\frac{C_{\ket{DD}}+C_{\ket{AA}}+C_{\ket{HH}}+C_{\ket{VV}}-C_{\ket{HV}}-C_{\ket{VH}}+2\sqrt{C_{\ket{DA}}C_{\ket{AD}}}}{2N}.$
(S14)

##  VII Telecom Photon Loss Budget

Element | Loss (dB)
---|---
Input Paddles | 0.74
APC Injector | 0.22
Optical Switch | 0.52
APC Compensator & Optical Switch | 1.54

##  VIII Expected Entangled State Fidelity From Cross Correlation

Here, we derive an expression for the expected entangled state fidelity based
on the cross correlation function, $g_{SI}$, of a probabilistic pair source.
For the model we assume that the source produces perfectly entangled Bell
pairs (without loss of generality we shall assume
$\ket{\phi_{+}}=\frac{\ket{HH}+\ket{VV}}{\sqrt{2}}$) in addition to some white
noise. We may write the density matrix for the source output as

$\hat{\rho}=a\ket{\phi_{+}}\bra{\phi_{+}}+\frac{1-a}{4}\hat{\mathbb{I}},$
(S15)

where $a$ parameterizes the noise of the source output and $\hat{\mathbb{I}}$
is the identity matrix. The entanglement fidelity is calculated as

$F=\frac{1+3a}{4}.$ (S16)

The single polarization mode cross-correlation, $g_{SI}$, can be written as

$g_{SI}=\frac{\left<HH\right>}{\left<HV\right>}=\frac{1+a}{1-a}.$ (S17)

Re-arranging we find the expression quoted in the main text

$F=1-\frac{3}{2(1+g_{SI})}$ (S18)


# Assessing the Impact of Personality on Affective States from Video Game
Communication ††thanks: This work is funded by James S McDonnell Foundation
(Grant Title: A Methodology for Studying the Dynamics of Resilience of College
Students).

Atieh Kashani  Department of Computational Media
University of California, Santa Cruz
Santa Cruz, USA
<EMAIL_ADDRESS>Johannes Pfau  Department of Computational Media
University of California, Santa Cruz
Santa Cruz, USA
<EMAIL_ADDRESS>Magy Seif El-Nasr  Department of Computational Media
University of California, Santa Cruz
Santa Cruz, USA
<EMAIL_ADDRESS>
###### Abstract

Individual differences in personality determine our preferences, traits and
values, which should similarly hold for the way we express ourselves. With
current advancements and transformations of technology and society, text-based
communication has become ordinary and often even surpasses natural voice
conversations - with distinct challenges and opportunities. In this
exploratory work, we investigate the impact of personality on the tendency how
players of a team-based collaborative alternate reality game express
themselves affectively. We collected chat logs from eleven players over two
weeks, labeled them according to their affective state, and assessed the
connection between them and the five-factor personality domains and facets.
After applying multi-linear regression, we found a series of reasonable
correlations between (combinations of) personality variables and expressed
affect - as increased confusion could be predicted by lower self-competence
(C1), personal annoyance by vulnerability to stress (N6) and expressing anger
occured more often in players that are prone to anxiety (N1), less humble and
modest (A5), think less carefully before they act (C6) and have higher
neuroticism (N). Expanding the data set, sample size and input modalities in
subsequent work, we aim to confirm these findings and reveal even more
interesting connections that could inform affective computing and games user
research equally.

###### Index Terms:

Affective Computing, Individual Differences, Five Factor Model, Alternate
Reality Games

##  I Introduction

Communication is a complex subject that can be influenced by numerous factors
including individual differences and their emotional or affective states.
During a communication act, individuals express affects in different ways by
their choice of words, facial expression, vocal features, gesture and body
language. Both verbal and nonverbal cues play an important role in the way
that affect is expressed and interpreted through communication[1, 2]. With the
rise of digital media, communications are increasingly performed using text-
based computer-mediated communication. The lack of nonverbal cues in mediated
communication has led to the assumption that text-based communication has a
reduced capacity for exchanging affective states [3]. However, text-based
communication can convey various ranges of emotions and affects by adapting
the forms that are distinct from those found in non verbal communication [4,
5]. During text-based communication, communicators encode the emotions and
affects that they would normally communicate through nonverbal cues into the
other forms such as emoticons, deformed spellings, punctuation, acronyms and
special abbreviations[6, 7, 8]. In addition, synchronous real-time text
communication can capture some of the synchronicity that is associated with
voice or face-to-face communication [9]. Thus, the emergence of real-time and
online communication platforms has created new avenues for studying the verbal
behaviour phenomenon and its psychological correlates.

Individual differences refer to the variations that exist between humans with
regard to personality, cognition and behaviours. Personality has been defined
as ”a stable, organized collection of psychological traits and processes in
the human being that influences his or her interactions with and modifications
to the psychological, social and physical environment surrounding them” [10].
The different personality traits can manifest in various ways including how
individuals experience and express affects or emotions in verbal
communication. The Five Factor Model (FFM) [11] is the most accepted and
widely used personality theory that provides a systematic assessment of
emotional, interpersonal, experiential, attitudinal, and motivational styles.
While the five overarching domains of the FFM are too broad to capture the
complex human personality in detail, underlying individual facets form a more
precise description of personality to differentiate between individuals and
their behaviours, including the expression of affects [12].

Video games have the potential to place individuals in the continuous mode of
interaction that evoke emotional and affective responses. Players are drawn to
play games not only for enjoyment and achieving rewards but also for engaging
in experiences that may even elicit negative emotions like sadness, anxiety,
and frustration[13]. Game features such as mechanics, interactive gameplay,
storyline and immersive graphics make them a unique platform in affective
computing research[14] for studying psychological constructs and social
phenomena. In particular, Alternative Reality Games (ARG) can construct a
close connection to reality, as they embed players in a fictional narrative
that unfolds through interaction with real-world applications, such as mobile
phones, text messages and social networks [15]. In ARGs, the interactions and
in-game events often mimic real life situations that can engage participants
for an extended period of time. Utilizing ARGs allows researchers to
incorporate engaging and ecologically valid methods to study various aspects
of human behavior by capturing multi-dimensional data on humans’ interactions
and communications.

Altogether, this creates a unique opportunity to study the impact of
personality on verbal expression of affects set in ARG-mediated communication,
which we approach in this work. Investigating the connection between
personality and expression of affect can lead to several potential benefits
such as more inclusive design, adaptive personalization and tailored
interventions through understanding individual differences. Thus, we formulate
our research endeavor into the following research question:

  * •

Can we identify connections between individual personality differences and the
tendencies to express oneself in distinct affective categories from in-game
chat conversation?

By exploring and presenting initial relations between personality and affect
expression through game communication, we contribute to games user research
and affective computing.

##  II Related Work

Previous studies show that the expression of emotions or affects in
conversation varies as a function of individual differences and personality
traits [16, 17, 18, 19, 20]. Holtgraves investigated the correlations between
the five-factor model of personality (extroversion, neuroticism,
agreeableness, conscientiousness, and openness to experience) and how it
impacted the use of language in text messaging [16]. He reported that
increased neuroticism was associated with the more frequent occurrence of
negative emotion words, higher scores on extroversion were associated with the
occurrence of fewer negative words, and agreeableness was negatively
correlated with the use of negative emotion words. Another study also found
that agreeableness is positively correlated with the occurrence of positive
emotion words and negatively with negative emotion words [20]. Komulainen et
al. reported that conscientiousness positively associate with positive affect
and negatively associate with negative affect [18]. Consistent with previous
findings, recent studies show that individuals high on self-reported
extroversion tend to use more positive emotion words [21] and individuals high
in conscientiousness demonstrate their prudence by refraining from expressing
negative emotions [22].

For different application purposes, Volkmar et al. tailored in-game
achievements to individual differences and measured an increase of player
experience if matching properly [23]. Teng et al. used player journey map
segmentation to investigate differences in gameplay based on – or influencing
– higher-level metrics, which are not limited to personality variables [24,
25]. Habibi et al. measured differences in physiological responses between
different personalities, especially higher impact of stress on more
extroverted persons [26]. In subsequent work, they also predicted individual
personality differences from low-level in-game behavior and (pre-defined)
communication choices [27], which were yet far from unconstrained, natural
speech.

The mentioned studies considered only five factors of personality traits and
none of them examined how facets manifested in natural text-based
communication. In addition, these studies reported the impact of personality
traits on the broad emotional or affective states (positive and negative).
Therefore, the specific and discrete expression of emotions and affects were
not examined.

The current study attempts to address those limitations by utilizing a serious
ARG to examine how the occurrence of expression of distinct affects in verbal
communication varies as a function of individuals’ personality traits and
facets.

##  III Study

To situate our investigation into a suitable Alternate Reality Game, we draw
on the game called LUX [28], which was developed and the data were collected
by a group of researchers and developers with the aim of measuring resilience
and coping strategies in first-year undergraduate students. LUX is a
multiplayer team-based cooperative game designed to foster communication
within solving complex puzzles and challenges. It is set in a fictional
narrative and takes place and interacts with the real world, while presenting
challenges and stressors to assess emotional and affective responses. The game
is composed of multiple episodes, and each episode consists of a series of
puzzles in which players need to communicate with a bot and other team members
through Discord in order to solve them. We collected the players’ chat data,
identified affective states throughout the messages and linked them to their
self-reported FFM personality variables (cf. Section III-A).

###  III-A Measures

For measuring the participants’ personality, we have utilized the Revised NEO
Personality Inventory (NEO PI-R) [12] as the standard self-report
questionnaire measure of the Five Factor Model (FFM), which provides a
systematic assessment of emotional, interpersonal, experiential, attitudinal,
and motivational styles. The NEO PI-R is a concise measure of the five major
domains of personality (Neuroticism, Extraversion, Openness, Agreeableness,
and Conscientiousness). Within each of those broader domains, six specialized
traits (facets) together represent a given domain score (which add up to 30
facets in total).

For qualitative classification of the chat data, we have employed Plutchik’s
Wheel of Emotion [29] and the taxonomy of affects as discussed by [9] to
develop a set of labels. In total, we ended up with ten labels as outlined in
Table I. This label set was then utilized to label the players’ conversation.
. We also considered a “no affect” label to exclude messages that do not
express any affective state. For this investigation, one researcher served as
an annotator for all players’ conversations. They considered the impact of the
situational context and surrounding messages in the conversation to apply the
code that captures the affect expressed in the message. They also took into
account the impact of verbal cues such as emojis, slang and abbreviations that
influenced the affective meaning of the entire sentence. In some cases, these
did express actual affects, or were used to avoid misleading others (e.g.
after being sarcastic). A total number of 3748 lines of utterances has been
labeled line by line, with up to one affective label each.

Label |  Description |  Chat data example
---|---|---
Agreement |  Being consistent with or accepting other player’s opinions or plans towards finding clues and solving puzzles |  “alright sounds good”
Confusion |  Lack of certainty when encountering a situation associated with the game or puzzle |  “I’m not sure if the scans are allowed to be connected to each other ): because so far none of them have..”
Disagreement |  Lack of consistency in players’ opinions or plans in the game or during the process of solving puzzles |  “really don’t think it’s Octavian”
Excitement |  Feeling eagerness towards a progress or an intense response as a result of an accomplishment in the game |  “LETS GOOO”
Frustration |  Feeling of dissatisfaction or hopelessness as a result of failure, being stuck, encountering problems or inabilities to find clues or solve puzzles |  “unfortunately, i just get a bunch of garble”
Amusement |  Finding an incident funny during game play or in the process of solving puzzles |  “hey, work smarter, not harder lol”
Supportive |  Being collaborative and providing help to assist the teammates to find clues or solve puzzles |  “I’ll scan that when I get home”
Annoyance |  Feeling unpleasant or irritated as a result of failure or inability to find clues or solve puzzles |  “ugh is this ispy?”
Interest |  Feeling of wanting or giving attention to the situation associated with the game or puzzle |  “i want to make sure i get through it, so id like to schedule”
Anger |  Intense emotional response as a result of failure, being stuck, or encountering with a problem in the game in the process of solving puzzles |  “Damn we broke the bot”

TABLE I:  Set of affect labels from Plutchik’s wheel of emotions that appeared
within the conversation of the game, together with their definition and an
example from the data.

###  III-B Procedure

We recruited participants through an on-boarding event on campus, where they
agreed to informed consent and data collection. We then asked participants to
form a team with three members to start the game, resulting in five teams in
total: four teams with three members each and one team with four members. A
total of 16 players played the game through two weeks of playtesting, and
submitted a post-study questionnaire containing the discussed metrics
afterwards. Yet, one team with four members did not finish the game and
another single player failed to submit the NEO personality questionnaire,
which we excluded from further investigation. From the remaining eleven
players, six identified as male and five identified as female, distributed
into four teams.

##  IV Results

We applied a multi-linear regression model using Python Scikit-learn library
and analyzed the data to predict the occurrence of each affect based on a
personality domain/facet or a combination of up to four personality
domains/facets. To evaluate the results of the prediction, we calculated the
Mean Square Error (MSE) values for each personality facet/domain combination.
Table II shows the combination of personality domains/facets that can predict
the conversational affect occurrence with highest accuracy (lowest MSE) after
five-fold cross-validation. In addition, we calculated the coefficient
associated with each particular personalty domain/facet to assess the
direction and effect size onto the expressed affect. To benchmark these
outcomes against a control condition, we considered two baselines that follow
assumptions that personality would have no impact on the prediction of affect.
In the first, the possibility of the occurrence of each affective state in the
conversation is equal for all the affects. Considering the ten different
affective states in our sample, the probability of occurrence of each affect
states in conversation is thus 10%. The second baseline acknowledges that
different affective states are differently likely to appear in the data and is
thus constructed based on the mean of the total occurrence of each affect in
our sample (cf. columns BL1 and BL2, respectively). Since the number of the
“Supportive” affect label in the players’ conversation is higher than the
other affect labels, the naïve BL1 and BL2 would show especially high MSE in
contrast.

The results showed that the combination of four personality domains/facets
predict the conversational affect occurrence with highest accuracy (lowest
MSE) on the testing set. We included the top three combinations together with
their coefficient towards the affective state. For example, when predicting
the occurrence of “Anger”, the combination of “Anxiety”, “Modesty”,
“Deliberation” and “Neuroticism” had a comparatively low MSE of 0.84, as
compared to the two baselines ($MSE_{BL1}=60.6$ and $MSE_{BL2}=9.8$). When
taking the coefficients into account as well, personalities with higher
“Modesty” and “Deliberation” indicated less expressions of “Anger”, while
higher “Anxiety” and “Neuroticisim” correlated rather positively with “Anger”.

Affect | Personality Domains/Facets (and Coefficients) |  | MSE
---
(LR)
| MSE
---
(BL1)
| MSE
---
(BL2)
| O4: Actions (1.34) | A1: Trust (-1.57) | C1: Competence (0.83) | N: Neuroticism (-0.19) | 1.63 | 21.4 | 13.1
Agreement | C1: Competence (-0.84) | C3: Dutifulness (-1.16) | C4: Achievement (-0.99) | O: Openness (0.64) | 2.54
| O4: Actions (1.18) | A1: Trust (-1.13) | C3: Dutifulness (-0.27) | N: Neuroticism (-0.12) | 3.04
| E5: Excitement (-0.77) | C1: Competence (-1.96) | N: Neuroticism (-0.47) | O: Openness (0.74) | 4.16 | 54.6 | 50.4
Confusion | O6: Values (4.47) | A3: Altruism (8.37) | A6: Tender-Mind. (-2.5) | E: Extraversion (-0.66) | 4.60
| N6: Vulnerability (-1.98) | O3: Feelings (1.87) | A4: Complicated (0.88) | C1: Competence (-3.03) | 6.9
| E5: Excitement (0.26) | O2: Aesthetics (0.14) | O5: Ideas (-0.40) | O6: Values (0.74) | 0.11 | 80.4 | 2.9
Disagreement | E2: Gregariousness (-0.30) | E3: Assertiveness (0.53) | O1: Fantasy (0.73) | O4: Actions (-0.19) | 0.16
| N2: Anger Hostility (0.10) | O5: Ideas (-0.32) | O6: Values (0.63) | E: Extraversion (0.09) | 0.17
| N2: Anger Hostility (-1.0) | A3: Altruism (0.92) | C2: Order (-0.57) | A: Agreeableness (-0.24) | 0.78 | 44.1 | 9.9
Excitement | N2: Anger Hostility (-0.9) | E2: Gregariousness (0.78) | C2: Order (-0.78) | A: Agreeableness (-0.14) | 0.81
| N2: Anger Hostility (-0.62) | E2: Gregariousness (0.82) | C1: Competence (-0.35) | C2: Order (-0.82) | 0.89
| E6: Pos. Emotions (1.02) | O2: Aesthetics (0.37) | A2: Straightfwd. (-0.33) | A3: Altruism (0.7) | 0.10 | 45 | 8.6
Frustration | E6: Pos. Emotions (0.83) | O2: Aesthetics (0.38) | A3: Altruism (0.78) | A6: Tender-Mind. (-0.31) | 0.47
| E6: Pos. Emotions (0.91) | O2: Aesthetics (0.43) | A3: Altruism (0.87) | A: Agreeableness (-0.12) | 0.44
| E2: Gregariousness (2.21) | C1: Competence (-1.06) | C2: Order (-2.61) | A: Agreeableness (0.41) | 3.08 | 55.6 | 58.4
Amusement | N1: Anxiety (0.97) | N2: Anger Hostility (-1.91) | C2: Order (-1.26) | C5: Self-Discipline (-1.55) | 3.48
| E3: Assertiveness (1.35) | A1: Trust (-1.36) | C2: Order (-2.17) | A: Agreeableness (0.80) | 4.32
| C1: Competence (4.6) | N: Neuroticism (0.72) | O: Openness (2.36) | C: Conscientious (1.2) | 15.63 | 1551.3 | 401.3
Supportive | N3: Depression (3.66) | A1: Trust (1.45) | A5: Modesty (7.48) | O: Openness (-1.99) | 20.33
| E1: Warmth (-7.51) | O4: Actions (-2.93) | C1: Competence (8.66) | C6: Deliberation (6.33) | 34.72
| N6: Vulnerability (1.48) | E1: Warmth (-2.96) | A2: Straightfwd. (1.41) | A5: Modesty (-1.29) | 3.04 | 60.5 | 25.7
Annoyance | E5: Excitement (1.55) | E6: Pos. Emotions (-1.21) | O3: Feelings (-1.55) | O6: Values (1.16) | 3.80
| N5: Impulsiveness (-1.18) | E2: Gregariousness (1.76) | O3: Feelings (-2.07) | C4: Achievement (1.95) | 6.99
| E6: Pos. Emotions (-0.35) | O1: Fantasy (0.78) | A5: Modesty (0.78) | C5: Self-Discipline (-0.13) | 0.12 | 57.5 | 3.5
Interest | E1: Warmth (0.26) | E6: Pos. Emotions (-0.39) | O1: Fantasy (0.79) | A5: Modesty (0.66) | 0.14
| E6: Pos. Emotions (-0.32) | O1: Fantasy (0.76) | A4: Complicated (0.09) | A5: Modesty (0.70) | 0.17
| N1: Anxiety (0.35) | A5: Modesty (-1.86) | C6: Deliberation (-1.81) | N: Neuroticism (0.25) | 0.84 | 60.6 | 9.8
Anger | O5: Ideas (-0.43) | O6: Values (0.97) | A6: Tender-Mind. (-0.59) | C4: Achievement (0.32) | 0.87
| N6: Vulnerability (-0.36) | O6: Values (0.47) | C4: Achievement (0.86) | A: Agreeableness (-0.39) | 0.9

TABLE II: Most accurate personality domains/facets to predict affective
conversation after multi-linear regression (indicating coefficients and mean
squared errors), as compared to a baseline that assumes every label would
appear equally (BL1) and a baseline that includes the different distributions
of affects in conversation, but neither regards the impact of personality on
the prediction (BL2).

##  V Discussion

When interpreting the results of the prediction (as summarized in Table II),
certain relationships could be identified that are arguably reasonable, while
others do not necessary align with the background literature, or display
inconclusive results, which we outline in the following. Although we attempted
to support our findings with relevant psychological literature, we encountered
a lack of sufficient research in some areas. Therefore, we proceeded with
interpreting the outcomes.

“Confusion” was best predicted by the personality facets of E5, C1, N and O.
The strong negative correlation between a person’s perceived self-competence
(C1) and the probability to be confused by a logical puzzle of the game seems
coherent. Also, as this method does not necessarily measure confusion itself
but rather the chance of expressing that one is confused (in comparison to
other personalities), it is reasonable that this willigness to admit one’s own
confusion goes along with higher Openness (O) and lower Neuroticism (N) in
general.

Individuals who are more vulnerable to stress (N6) also expressed to be
“Annoyed” more often. Same holds for people with less emotional warmth (E1)
and less modesty or humbleness (A5), which definitely stands to reason. This
is only underlined by the positive correlation to straight-forward
personalities (A2), as they are arguable less likely to withhold their
frustration.

“Anger” is positively correlated with the proneness to anxiety, worriedness
and nervousness (N1), which make up reasonable predictors for this. This is
similarly justifiable as with the connection to players that are less humble
and modest (A5), think less carefully before they act (C6) and have higher
Neuroticism (N) in general.

The likelihood of expressing more “Supportive” statements is highly correlated
with an individual’s perceived self-competence (C1), as players could probably
give better support when understanding the current challenge themselves. The
connections to high openness towards other people (O) and high
conscientousness (C) similarly play well into this, while a positive
connection to Neuroticism (N) remains at least debatable.

The tendency to experience anger, frustration and bitterness (N2) consistently
correlates negatively with players that expressed their “Excitement” more
often, which arguably makes sense. Same might hold for personalities that
highly value other people’s welfare and experience (A3) or tend to be less
organized (O2). Yet, one would have hypothesized that the personality facet of
seeking excitement (E5) would also have a stronger connection to the
expression of “Excitement” throughout chat data.

Gregarious people enjoy the company of others (E2), which explains the high
correlation with their expressed “Amusement”. The negative correlation of
self-perceived competence (C1) and expressed amusement is however debatable,
as there is no simple linear connection between objective ability (or
subjective competence) and happiness [30].

The tendency to experience positive emotions (E6) is highly predictive of the
players’ expressed frustration, which does not compute at first glance, yet
the facet does not exclude the experience of negative emotions per se. This
correlation could still stand to reason for people that are generally more
prone to experience both negative as well as positive emotions, but a
connection to facets that particularly target negative emotions would have
been more reasonable.

However, at least with regards to background theories, we cannot justify the
correlation between “Disagreement” and people who are more excitement-seeking
(E5), or personalities that have a deep appreciation for art and beauty (O2).
In fact, the traits that indicates the openness to accepting new ideas and
other opinions (O5) is negatively correlated with “Disagreement” in these
results, where the opposite would be more intuitive.

Thus, we engage with our introductory research question, arguing that we
delivered initial insights that individual personality differences can
strongly impact affective expression in game communication, and that most of
the derived connections are reasonably justifiable, barring some limitations
that are discussed in the following.

##  VI Limitations and Future Work

Altogether, most of the predicted multi-linear correlations stand to reason,
with some exceptions that are presumably caused by the highly noisy domain of
individual personality. For the sake of brevity, we did not explicate on all,
but only the most predictive facet combinations, and leave remaining
interpretations open for the reader through Table II. Certain connections that
we hypothesized to be trivially true (such as the tendency of agreeableness
(A) and the expressed “Agreements”, the personal desire for excitement (A5)
and the expression of it, or the hostility towards Anger (N2) and its
utterance) were not reflected in the prediction. Yet, we only considered the
four major factors that could predict the affect expression in the end, while
the former still might have had a smaller effect.

In our current labeling process, we only appointed a single annotator to
decide affective labels for the particular chat utterances. While this could
already show a working trend of the approach that can come up with reasonable
results, personal bias might have influenced the classification of the
conversations, which is why we are expanding this process in the next
iterative step of this work to multiple annotators and a proper assessment of
the inter-rater reliability.

An essential part of the noise that led to the inconclusive parts of the
results could be overcome by incorporating a larger data set of participants,
which is what we are currently working towards. Especially the highly
variational personality data requires a broad range of different personality
combinations in order to come to conclusions that are accurate and usable for
large-scale applications. Using in-game and conversational behavior from a
vast community of players of Sky: Children of the Light [31], we are striving
to scale our approach and investigate if we can extract comparable or even
more accurate findings.

The proposed technique is obviously limited in its applicability to domains
that incorporate recorded chat communication. This constrains it to multi-
player environments, and only those who actively engage humans in natural
language conversation. Yet, with the current rise of large language models and
increasing use of novel application cases, we are interested to investigate
single-player games that embed natural language conversations with non-player
characters for narrative, quest or mechanical reasons, and will derive if
there are significant differences in emotional expression when interacting
with artificial agents instead of fellow human players.

Eventually, for this proof of concept that reasonably accurate connections
between personality and affect expression through chat are derivable, we only
considered a single method for the modeling process. While the outcomes of the
multi-linear regression are intuitively understandable, more sophisticated
machine learning approaches could have approximated this connection with even
more accuracy. Thus, our future work includes the investigation of such
models, while we constrain ourselves to techniques with high explainability
(such as random forest regression or Bayesian belief networks) to still be
able to ground and justify the underlying functions (in contrast to black-box
models).

Limitations with respect to the ethical component of using this and related
methodologies are further discussed in Section VIII.

##  VII Conclusion

Individual personality differences influence how we make decisions, take
stances, display emotions and express ourselves. Video games, especially when
incorporating or being based on communication, have the opportunity to engage
players in conversation, control topics and insert stimuli, record context-
sensitive utterances and can even benefit from assessing affective states of
their players to tailor content, difficulty or experiences. Thus, this work
explored how the personality of players of a multi-player alternate reality
game impacted their expression of affective states when solving puzzles and
coordinating with their teams. By classifying their communication into
affective labels and modeling the role of their Five Factor Model facets
towards that, we present initial results that identify a first differentiation
between individuals and their expression of affect in text-based
communication. We considered ten primary conversational affects from
Plutchik’s established wheel of emotions and a combination of up to four
facets/domains, which often led to reasonable connections between personality
and affective expression already. Based on this, we are looking forward to
investigate large-scale observations between personality and expression, how
to accurately model these in the context of games, and how to make avail of
these to tailor player experiences through difficulty, content and
matchmaking.

##  VIII Ethical Statement

The realized study closely followed procedure, framing and informed consent as
approved by the institutional review board of the authors’ affiliated
university.

While this proposed technology aims at opening up understanding individual
differences and could tailor game mechanics, environments or matchmaking
towards inclusiveness and accessibility, it still bears certain risks and
ethical implications that should be addressed. First of all, as this approach
is working on conversation data which can be highly sensitive and personal,
the question of data ownership comes into play. Even if companies provide game
environments and services and therefore often have control over incoming and
outgoing data, chat data should ideally only be leveraged with the actively
confirmed approval from the particular player (i.e. opt-in). Ideally, echoing
data transparency, players should have full insight and control over the
history of their chat logs, so that unwanted entries could be permanently
removed from storage and usage for the model. Moreover, even when being able
to control their individual input, regular users can hardly estimate the
impact of their data and how it could change in-game or higher-level decisions
that certain use cases could determine - thus, in the spirit of
explainability, users should be able to clearly follow the decisions of the
model, its outcomes and implications on their experience with the product.
After all, modeling relationships between chat, personality and affect and
(algorithmically) deriving decisions from that should only be deployed for the
benefit (e.g. improved experience) of the user, but bears the risk to be
exploited to further facilitate dark patterns of (game) design, such as taking
advantage of purchasing patterns or reinforcing addictive tendencies. These
risks excel in the case of erroneous decision making of the model, which could
steer the individual’s experience in the wrong direction or completely spoil
it. Thus, if such a model is used for tailoring or adapting any element, it
should only do if it can satisfy the prediction following a reasonable
confidence.

## Acknowledgment

LUX was developed and the data were collected by the group of researchers and
developers including Reza Habibi, Bjarke Larsen, Sai Siddartha Maram, Shweta
Sisodiya, Jonattan Holmes, Zhaoqing Teng, and Jessica Wei at the University of
California, Santa Cruz.

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