# Satellite-based Quantum Network: Security and Challenges over Atmospheric
Channel

Hong-fu Chou, Vu Nguyen Ha, Hayder Al-Hraishawi, Luis Manuel Garces-Socarras,
Jorge Luis Gonzalez-Rios, Juan Carlos Merlano-Duncan, Symeon Chatzinotas
Interdisciplinary Centre for Security, Reliability and Trust (SnT), University
of Luxembourg, Luxembourg
Emails: {hungpu.chou,vu-nguyen.ha,hayder.al-
<EMAIL_ADDRESS>
###### Abstract

The ultra-secure quantum network leverages quantum cryptography to deliver
unsurpassed data transfer security. In principle, the well-known quantum key
distribution (QKD) achieves unconditional security, which raises concerns
about the trustworthiness of 6G wireless systems in order to mitigate the gap
between practice and theory. The long-distance satellite-to-ground evolving
quantum network distributes keys that are ubiquitous to the node on the ground
through low-orbit satellites. As the secret key sequence is encoded into
quantum states, it is sent through the atmosphere via a quantum channel. It
still requires more effort in the physical layer design of deployment ranges,
transmission, and security to achieve high-quality quantum communication. In
this paper, we first review the quantum states and channel properties for
satellite-based quantum networks and long-range quantum state transfer (QST).
Moreover, we highlight some challenges, such as transmissivity statistics,
estimation of channel parameters and attack resilience, quantum state transfer
for satellite-based quantum networks, and wavepacket shaping techniques over
atmospheric channels. We underline two research directions that consider the
QST and wavepacket shaping techniques for atmospheric transmission in order to
encourage further research toward the next generation of satellite-based
quantum networks.

###### Index Terms:

Quantum key distribution, satellite communication, quantum state transfer,
wavepacket shaping modulation

##  I Introduction

To meet the growing global demand for broadband services, satellites offer the
unique ability to cover enormous geographic areas while requiring minimum base
infrastructure, making them an appealing alternative[1]. The ability to
connect quantum devices across long distances, considerably boosting their
inherent communication, network efficiency, and security, is made possible by
an examination of the state-of-the-art of the key components of quantum
networks[2]. By delivering quantum states containing critical information
through free space optical (FSO) channels, the authors in [3] reveal the
possibility of establishing global quantum networks. To achieve unconditional
security, quantum key distribution (QKD)[4, 5] secures a protocol that can
guarantee information security in theory between two remote nodes while
exchanging keys. QKD is the most thoroughly explored quantum communication
technology[6], and it has been used in both fiber and FSO channels. Long-
distances FSO quantum communications[7, 8, 9] have been deployed effectively
across extraordinarily long distances while several experiments have also been
realized in [10, 11, 12]. However, when channel attenuation and noise levels
increase in the communication via fiber or FSO, the communication range for
successful key distribution is restricted to a few hundred kilometers. That
raises a significant challenge in satellite-based QKD systems. Recently,
quantum teleportation[13, 14, 15, 16] has been considered as a possible
approach for increasing the deployment range of QKD using satellites. By
moving to free space and connecting two ground stations, the effective
communication range can be increased to a hundred km; while connecting a
ground station with a satellite, quantum teleportation was conducted across a
thousand km. Although channel noise has no direct effect on the transported
qubit, it does result in an entanglement network with low fidelity,
diminishing the success chance of secret key transmission by quantum
teleportation[17]. Furthermore, while QKD theoretically provides ultra-
security to satellite-based QKD networks, satellite-to-ground, and inter-
satellite quantum communication systems, the exploitation of defects in
quantum cryptography protocols to undermine information security or obtain
unauthorized access to sensitive data is referred to as quantum hacking[18,
19, 20]. The physical layer security deduces that the efficiency for detecting
binary bit levels is identical, this raises doubts about the validity of the
security proof. The time-shift attack makes use of a QKD system’s time-domain
detection efficiency discrepancy between its two detectors. It is only
possible to securely eliminate the time-domain inconsistency of detection
efficiency. Therefore, the characteristics of the atmosphere can have
identical security concerns and are the critical instance required to consider
and investigate.

Starting with a background study of atmospheric channel characteristics
carrying quantum states and progressing to research challenging issues, the
goal of this paper is to bring up some more in-depth investigation by
reviewing and proposing open challenges of physical layer transmission and
security via satellite-based QKD networks, which will necessitate developing
more secure and efficient scenarios to achieve high-quality quantum
communications. We hope to explore the following significant implementation
issues as a result of this:

  * •

It is critical to investigate system design for the satellite-based quantum
networks over atmospheric channels in order to assure optimal system
performance, as well as approaches for diversified scheduling for space
missions or satellite-to-ground communication.

  * •

Because interference issues caused by coexistence with other satellite
systems, as well as atmospheric turbulence and diffraction, affect the
fidelity of satellite-based quantum networks, developing novel strategic
deployment and interference mitigation techniques is critical.

  * •

By using quantum mechanical ideas in QKD networks, the quantum states based on
a variety of QKD protocols, as well as the heterogeneity of transmissivity
from satellite-to-ground/air/space-destination scenarios to the aforementioned
deployments, can be realized. As a result, channel parameter estimation is
indispensable in such dynamic satellite communication.

  * •

Experiments show that the assaults against a commercial QKD system are
technically feasible. Because of these minor flaws, satellite-based QKD
networks may be susceptible to Eve with current technology. The effectiveness
of the attacks emphasizes the need to develop innovative techniques for
security proofs with verifiable premises and battle-test actual resilience to
any attacks.

Additional prospects for satellite-based quantum networks and potential future
research topics are also included in this paper.

##  II Quantum networks via Atmospheric Channel

We start from a basic knowledge of quantum states in QKD networks and
atmospheric channels to the potential future research avenues.

###  II-A Entangled Gaussian and Non-Gaussian States

Continuous variables Gaussian states, such as thermal, coherent, and
compressed states of light, are one example of states that cannot be purified
by ordinary processes[21]. When ordinary processes are referred to, the
actions that keep the state’s Gaussian characteristics intact are implicit in
matching mirrors, beam splitters, and squeezers. Therefore, any entangled
Gaussian state has bound entanglement in the Gaussian assumption. The
symplectic matrix allows for a compact expression of the canonical commutation
relations (CCR)[21] for a quantum system with n modes. Gaussian two-mode
squeezed vacuum (TMSV) states are characterized by a gaussian $\chi_{\rho}$
function.

$\chi_{\rho}(\zeta)=e^{i\zeta^{T}J_{n}d-\frac{1}{4}\zeta^{T}J_{T}^{n}\gamma
J_{n}\zeta}$ (1)

where d is a $2n$ real vector, called displacement vector (DV), and $\gamma$
is a $2n\times 2n$ symmetric real matrix, denoted as the covariance matrix
(CM). Researchers[22] apply the scenario of prepare and measure with
compressed or coherent states to experimentally build quantum cryptography
with gaussian states and gaussian operations to discuss the efficiency of
security protocol.

Implementing non-Gaussian entangled states effectively across atmospheric
fading channels is still difficult while maintaining a reliable secret key
rate. Recent research has looked at the rate of entanglement formation caused
by non-Gaussian entangled states moving through atmospheric channels [23, 24].
A non-Gaussian entangled state [24] can be addressed by giving a Gaussian
state and zero first moment CM by

$M_{AB}^{in}=\begin{bmatrix}vI&\sqrt{v^{2}-1}Z\\\ \sqrt{v^{2}-1}Z&vI\\\
\end{bmatrix}$ (2)

where $I$ is a $2\times 2$ identity matrix, Z is a $(1,-1)$ diagonal matrix,
and $v=cosh(2r)$ is the quadrature variance of each mode. The pure photon-
subtracted squeezed (PSS) state is introduced to the unmeasured output of the
beam splitter in order to elicit this operation of non-Gaussian states by
detecting heralded modes. This transfer is then analyzed by using the Kraus
representation to chart the PSS state’s progress through the fading channel.
The authors[24] investigate that contrary to common sense, non-Gaussian states
can occasionally yield greater quantum key rates via fixed-attenuation
channels and particularly for very high-loss channels. Furthermore, the
measurement result[25] is determined using a coherent detector at the receiver
using an upgraded non-Gaussian state discrimination detector. The received
nonorthogonal coherent states are measured with the state-discrimination
detector, which is regarded as the optimal quantum measurement[25]. High
uplink losses are frequently an issue for satellite-based communication
systems. Without the helpful intervention, satellite-based entanglement
distribution and quantum key distribution would remain an unsuccessful
undertaking. Therefore, we discuss the atmospheric channel loss in the next
section.

###  II-B Channel Loss of Satellite-based quantum networks

For the satellite-based QKD networks, the uplink and downlink channels are
quite different. On an uplink channel, the atmospheric turbulence layer only
occurs close to the transmitter, while on a downlink, it only exists close to
the terrestrial receiver. The uplink optical beam initially travels through
the turbulent environment for typical ground station aperture sizes, and its
beam-width is substantially smaller than the large-scale turbulent vortex. The
downlink optical beam only passes through the turbulent environment during the
last portion of its route, in contrast to the uplink channel. The satellite’s
beam-width upon entrance into the atmosphere is most likely to be greater than
the size of the turbulent vortex given the usual aperture size of the optical
equipment incorporated in the satellite. Therefore, turbulence-induced effects
[6] cause the transmissivity, $\eta_{t}$, of atmospheric channels to change.
The probability distribution of the transmission coefficients, indicated by
$p(\eta)$, may be used to describe these fading channels where
$\eta=\sqrt{\eta_{t}}$. The mean fading loss in dB for a channel that is
fading and associated with the probability distribution $p(\eta)$ is given by
$-10log_{10}\int_{0}^{\eta_{0}}\eta^{2}p(\eta)d\eta$, where $\eta_{0}$ is the
greatest value of $\eta$. Another dominant of the loss is beam-wandering which
causes the beam-center to wander erratically from the receiver’s aperture
plane, regardless of atmospheric turbulence-related changes in beam-width[6].

When beam-width variations are taken into account, the mean fading loss in dB
of a fading channel is now given by
$-10log_{10}\int\eta^{2}(l,\theta)p(l,\theta)dld\theta$ with the knowledge in
[6]. It should be noted that, with the addition of beam-width variations, the
channel’s maximum transmission coefficient $\eta_{0}$ is no longer constant
but instead varies at random. Therefore, the above introduction can lead us to
the research in [26] to investigate Gaussian entangled states in fading
channels and uncorrelated fading channels. The transmitted continuous-variable
entanglement has a non-trivial effect on coherent displacements of the input
field’s quantum state in such turbulent channels. Surprisingly, this enables
one to maximize the entanglement certification by altering local coherent
amplitudes with a limited but optimal amount of squeezing. These variables can
be changed to enhance the Gaussian entanglement transfer via a turbulent
environment by adaptive method attaining the correlated form in the
entanglement preserving link. Following this thread, the long-range quantum
state transfer is presented in the following section.

###  II-C Long-distance Quantum State Transfer

Many quantum information processing (QIP)[27] activities rely on the transport
of quantum information between various sites. The quantum state transfer
(QST)[28] of interacting qubits might be significantly more advantageous, both
for the QIP protocol and for transmitting the entire physical configuration of
quantum communication. Long-distance QST is an important component of quantum
protocols that can be realized by quantum teleportation. The challenges of
long-distance QST[29, 30, 31] are to maintain the fidelity and reduce the low
fidelity caused by inconsistency of the channel’s mirror symmetry. Moreover,
in prior long-distance investigations, Alice and Charlie have always performed
local Bell-state measurements before the entanglement distribution procedure.
It is difficult to conduct the Bell-state measurement after photons pass via
air channels due to atmospheric turbulence. The authors in [32] prove the QST
over a distance of more than 1000 km with the satellite Micius aided by
previous quantum entanglement shared between two distant ground stations. The
highly steady interferometer project the photon into a composite path-
polarization dimension and makes use of a satellite-borne entangled photon
source.

##  III Open Challenges

Based on the extensive approaches for making quantum states adapt to
atmospheric channel variations, we identify the following challenges in order
to increase fidelity and security resilience, more research efforts should be
addressed for greater robustness to actual attacks, as well as the inspiration
for a better understanding of quantum state correlation in the atmosphere. We
depict the quantum networks in Fig. 1 to illustrate the following challenges.

Figure 1: A Vision of Satellite-based Quantum Networks.

###  III-A Transmissivity Statistics on Atmospheric Channels

Extensive theoretical examinations[33, 34, 35] of these effects are presented,
and these models are shown to be broadly coherent with terrestrial testing
done under a broad range of turbulence conditions. The quantum states of
entanglement conditions were explored in [33, 36, 37] based on the negativity
of the partial transposition. In order to implement and optimize quantum
communication in atmospheric connections, the partial transposition can be
viewed as the output state of turbulent atmospheric fluctuating-loss channels.
Despite the dominating impacts of the variable nature of transmissivity in
these channels, which introduces extra noise and limits the possible secret
key rate, other more subtle atmospheric effects such as weather condition[38,
34] and day-and-night times[15], which consider beam attenuation, absorption,
and scattering, can play a significant role[39, 24, 23, 40]. We illustrate in
Fig. 1 the case of satellite-based QKD node 1 communicating with the ground
user terminal and long-range communication between satellite-based QKD node 1,
2, and 3. The collaboration of satellite-based QKD node 2 and 3 communicates
to the ground user terminal in distance QLAN. Due to the above discussion, QKD
networks are very sensitive to the channel’s transmissivity even during day-
and-night times. A thorough understanding of atmospheric channels[41, 15, 42]
has broad implications for research, and utilizing satellite-based nodes and
quantum ground transceivers with the bulk of propagation occurring outside the
Earth’s atmosphere can enable global-scale quantum communication. Furthermore,
transmissivity and secrete key rate can be aided by self-compensating
technique[9, 43, 44] such as some use cases of passive polarization analysis
units, adaptive optics pre-compensation, GPS timing receivers for
synchronization, and custom-written software. This research trend is still in
the initiative stage, and thus, more sophisticated approaches are necessary to
optimize the satellite-based QKD networks. Additionally, it is noteworthy to
remark that the authors in [45] present an interesting framework for
monitoring the continually changing satellite-to-ground atmospheric channel.
This framework aspires to enhance the scheduling techniques by optimizing the
available time for SatQKD and reducing the average link loss during a single
orbit. The suggested scheduling technique serves the dual objective of
reducing geometric loss in future satellite orbit selection and enhancing the
effective use of designated keys.

###  III-B Estimation of Channel Parameters and Attack Resilience

The general idea of the design requirement for satellite-based QKD networks is
that because of the changing nature of transmissivity in these channels, more
noise is generated, limiting the feasible secret key rate. A thorough
framework for analyzing the needs for spatial, spectral[46], and temporal
filtering is provided by the study[47, 48] for wavelength-dependence free
space QKD networks. However, an adaptable paradigm for optimal wavelength is
required more effort to provide high performance. Despite the practical attack
on QKD networks[18], channel parameter estimation is not only beneficial to
secret key rate performance[49, 50, 51, 52] but also security concern [53, 54]
to demonstrate against entanglement-distillation attack. Eve may be undetected
by Alice and Bob utilizing basic light monitoring that is present in quantum
repeaters such as satellite-to-ground channels and ground-to-ground networks
in the event of this assault potentially generating a loophole based on the
assumption [55]. The Monte Carlo approach[53] was used to estimate the channel
transmittance, which changes randomly over time. Especially when there is
little knowledge of the channel, as there is in the case of the atmosphere and
the ocean, it is improper for parametric variation channels to be based on
insufficient statistical features. Authorized communication[25] is required to
continuously communicate partial input and output signals in order to update
the channel estimate when the channel changes, even if it changes slowly. As
illustrated in Fig. 1, both Eve 1 and 2 present the threat to demonstrate the
potential loophole between Alice and Bob. Moreover, malicious attackers in the
ground user terminal act as Eve 3 performing unauthorized access to QKD node
3. Above all, further research efforts must be made in order to investigate
both the secret key rate performance and the durability of the attack.

###  III-C The Quantum State Transfer for Satellite-based Quantum Networks

Following the discussion in Section II D, QST allows the transfer of arbitrary
quantum states from one node to another by SWAP[56] or quantum teleportation.
As illustrated in Fig. 1, the quantum state transfer exist over the atmosphere
for the satellite-based QKD networks. Moreover, spatial steering is well-known
that quantum states may be remotely created via an entangled pair to be
benchmarked by average fidelity[28]. It is worth noting that the study of a
quantum teleportation protocol in [16] presents a comprehensive investigation
of uplink and downlink channel loss mechanisms. This thread leads us to the
challenge of investigating the effectiveness of QST on atmospheric channels.
The authors in [57] first touched on this challenge. Regarding remote state
determination or remote state tomography, quantum information transfer
considers providing a quantum teleportation protocol and associated security
discussion with the QKD protocol by means of high-dimension quantum
correlations. Furthermore, the experiment results of quantum teleportation
[16] show improved fidelity by the generation of states in an intermediate
station that produces nearly symmetric states in line with the well-known
Braunstein-Kimble quantum teleportation process to have a better teleportation
fidelity. Furthermore, the authors in [58] provide the experiment of a given
event proving that the concurrence of entanglement can be conserved by
turbulent atmospheric channel. By demonstrating how to improve the fidelity of
QST or entangled transfer on atmosphere measuring prior to the privacy
amplification of satellite-based QKD networks, we highlight this potential
research avenue that can be taken into consideration in the physical layer of
quantum networks. In order to improve the secret key rate, transmissivity, and
fidelity for sophisticated satellite-based quantum networks, it is beneficial
to investigate the quantum state correlation and decoherence on atmospheric
channels, which depend on the implementation of entanglement transfer or QST.

###  III-D Wavepacket Shaping Techniques over Atmospheric Channels

Following the quantum state introduction of Section II A, an innovation
technique in [59, 60] observes the purification and entanglement after
conducting wavepacket shaping modulation to single photon and entangled photon
which is applicable to both single-photon and entangled-biphoton QKD devices.
The experiments in [59] demonstrates how the wavepacket modulation control
photons emitted from the colloidal quantum dots at room temperature. It has
been shown that biexciton emission is eliminated by modulating the wavepacket,
the emitted single photons preserve the high purity even at high excitation
power. Furthermore, the result of concurrence and purity shows that wavepacket
modulation reserve and restore the entanglement at the high-frequency
difference by topographically reconstructing the density matrix. However, this
shaping modulation applies to satellite-based quantum networks which remain
more explored and studied over atmospheric channels. Based on the purification
and revival entanglement to the quantum state, the implicit correlation with
long-range QST to the physical layer of the quantum network is still not clear
about how the photon absorption efficiency and revival of entanglement can
enhance the transmissivity and entangled quantum networks respectively. This
could be quite an interesting research direction to investigate for the
advanced design of physical layers in satellite-based quantum networks.

##  IV Conclusion and Future Directions

In order to enhance the quality of long-range quantum communication, this
paper reviews several significant technical evaluations of satellite-based
quantum networks and suggests future research options. First, the knowledge of
quantum states provokes the understanding of a fundamental transmission unit
for quantum communication. The atmospheric channel loss is explored to depict
the effect on coherent displacements and entanglement certification of the
quantum state. A more sophisticated self-compensating approach to receiver
design for satellite-based quantum networks can help to improve transmissivity
and secret key rate. The channel estimate is therefore seen as a challenge in
terms of both ensuring higher key transmission quality and thwarting possible
attacks. Based on the above reviews, this paper features two open challenges
that the implementation of QST and wavepacket shaping technique are required
to investigate how to improve the security, fidelity, and transmissivity of
satellite-based quantum networks and can be the potential candidates for
improving the existing approach to the challenges of estimating channel
parameters and attack resilience.

## Acknowledgment

This work is under the project LUQCIA funded by the European Union Next
Generation EU, with the collaboration of the Department of Media,
Connectivity, and Digital Policy (SMC), Luxembourg.

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