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IEEE photonics journal

Quantum Relay-Assisted Free-Space Optical Communication

Manav R. Bhatnagar, M. K. Arti, Kushagra Bhatnagar

Published Apr 22, 2025• 8 citations
Publisher

Abstract

Relay-based quantum communication utilizes intermediate nodes to extend the transmission distance of quantum signals and mitigate the masking effect caused by obstacles or turbulence in free-space optical (FSO) channels. In this study, we investigate a three-node quantum communication system, where Alice, the transmitter, sends quantum-encoded binary information to Bob, the ultimate receiver, via an intermediate relay node, Charlie. By introducing Charlie, the end-to-end transmission is divided into two shorter FSO links, improving signal stability and reliability in the presence of severe atmospheric turbulence and noise. This work proposes a quantum relaying method specifically designed for FSO links and examines the impact of two-hop relaying in terms of the probability of error. The Helstrom error bound is derived to assess the system's detection limits, while density operator calculations are performed to characterize the quantum relaying setup. In addition, a closed-form expression is obtained for key system performance metrics. The findings offer valuable insights into optimizing quantum relaying strategies for long-distance quantum communication over FSO channels.

DOI
10.1109/jphot.2025.3563374

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Relay-based quantum communication utilizes intermediate nodes to extend the transmission distance of quantum signals and mitigate the masking effect caused by obstacles or turbulence in free-space optical (FSO) channels. In this study, we investigate a three-node quantum communication system, where Alice, the transmitter, sends quantum-encoded binary information to Bob, the ultimate receiver, via an intermediate relay node, Charlie. By introducing Charlie, the end-to-end transmission is divided into two shorter FSO links, improving signal stability and reliability in the presence of severe atmospheric turbulence and noise. This work proposes a quantum relaying method specifically designed for FSO links and examines the impact of two-hop relaying in terms of the probability of error. The Helstrom error bound is derived to assess the system's detection limits, while density operator calculations are performed to characterize the quantum relaying setup. In addition, a closed-form expression is obtained for key system performance metrics. The findings offer valuable insights into optimizing quantum relaying strategies for long-distance quantum communication over FSO channels.
This paper develops a comprehensive analytical framework for a time-switching decode-and-forward quantum relay-assisted free-space optical communication system. In the proposed architecture, a batteryless relay harvests optical energy during a dedicated fraction of each transmission block and forwards quantum coherent states during the remaining time, enabling self-sustainable quantum relaying. Both hops are subject to Gamma-Gamma distributed atmospheric turbulence and additive Gaussian detection noise, while the relay and destination implement Helstrom-optimal quantum measurements that achieve the minimum symbol detection error. The framework unifies the effects of energy harvesting, turbulence-induced fading, and quantum-limited detection within a single performance model. Closed-form analytical expressions are derived for binary phase-shift keying modulation using the Helstrom bound, enabling tractable evaluation of the end-to-end error probability and the effective rate. The analysis establishes that the effective rate exhibits a strictly unimodal dependence on the harvesting fraction, yielding a unique optimal operating point that maximizes throughput under energy and noise constraints. Numerical results validate the theoretical findings and quantify the impact of turbulence severity, detection noise, and harvesting efficiency, demonstrating substantial performance gains over conventional non-harvesting quantum relays and providing new insights for energy-autonomous quantum optical networks.
This paper develops a comprehensive analytical framework for a time-switching decode-and-forward quantum relay-assisted free-space optical communication system. In the proposed architecture, a batteryless relay harvests optical en ergy during a dedicated fraction of each transmission block and forwards quantum coherent states during the remaining time, enabling self-sustainable quantum relaying. Both hops are subject to Gamma–Gamma distributed atmospheric turbulence and additive Gaussian detection noise, while the relay and destination implement Helstrom-optimal quantum measurements that achieve the minimum symbol detection error. The frame work unifies the effects of energy harvesting, turbulence-induced fading, and quantum-limited detection within a single performance model. Closed-form analytical expressions are derived for binary phase-shift keying modulation using the Helstrom bound, enabling tractable evaluation of the end-to-end error probability and the effective rate. The analysis establishes that the effective rate exhibits a strictly unimodal dependence on the harvesting fraction, yielding a unique optimal operating point that maximizes throughput under energy and noise constraints. Numerical results validate the theoretical findings and quantify the impact of turbulence severity, detection noise, and harvesting efficiency, demonstrating substantial performance gains over conventional non-harvesting quantum relays and providing new insights for energy-autonomous quantum optical networks
This paper investigates a quantum relay-assisted free-space optical (FSO) communication system in which a decode-and-forward relay is powered by time-switching optical energy harvesting and forwards the decoded information using displaced squeezed signaling (DSS). To obtain a physically con sistent description of turbulence-induced loss for non-classical signaling, each hop is modeled as a pure-loss bosonic chan nel whose random transmissivity follows a truncated Gamma Gamma law, i.e., the Gamma-Gamma irradiance conditioned on the physically admissible range of a transmittance. Under this channel, coherent states remain pure, whereas squeezed states are mapped to mixed Gaussian states. Under Helstrom-optimal detection, the average error of the coherent hop is derived in exact Laplace-series form. For the DSS hop, we derive the output states, a closed-form Gaussian fidelity with rigorous two sided bounds on the Helstrom error, and prove the existence of a loss-aware optimal photon partition. Furthermore, we prove that optimized squeezing preserves both the turbulence-induced diversity order and the leading asymptotic constant of coherent relaying, so that its benefit is a finite-photon-budget effect, and that an interior throughput-optimal harvesting fraction exists. A covariance-preserving benchmark with an exact series representation yields an analytical upper bound on the achievable throughput whose absolute gap vanishes as the relay photon budget grows. Numerical results based on the exact mixed-state Helstrom error quantify the benefit of squeezing and the regime in which it is useful.
Absorption, scattering, and turbulence experienced in underwater channels severely limit the range of quantum communication links. In this paper, as a potential solution to overcome range limitations, we investigate a multi-hop underwater quantum key distribution (QKD) where intermediate nodes between the source and destination nodes help the key distribution. We consider the deployment of passive relays that simply redirect the qubits to the next relay node or the receiver without any measurement. Based on the near-field analysis, we present the performance of a relay-assisted QKD scheme in terms of quantum bit error rate and secret key rate in different water types and turbulence conditions. We further investigate the effect of system parameters such as aperture size and detector field of view on the performance. Our results demonstrate under what conditions relay-assisted QKD can be beneficial and what end-to-end transmission distances can be supported with a multi-hop underwater QKD system.
This paper studies the design and performance analysis of relay-assisted satellite free-space optics (FSO) quantum key distribution (QKD) systems for secure vehicular networks. High-altitude platforms (HAPs) equipped with optical amplify-and-forward nodes are used as relay stations. Secrecy performances in terms of quantum bit error rate and ergodic secret-key rate are analytically investigated under the effects of transceiver misalignment, receiver's velocity variation, receiver noises, and atmospheric turbulence conditions. Based on the analyzed results, the design criteria for the legitimate user are determined so that the security of the considered system could be guaranteed.
In this letter, we analyze the average probability of error of quantum modulation schemes in weakly turbulent quantum communication channels utilizing coherent states. Atmospheric turbulence-induced fading is a significant challenge that degrades the performance of free-space quantum communication systems. We derive and present closed-form expressions for the average probability of error for various detection methods: classical (shot-noise limited) single-photon detection, coherent detection, and the optimal quantum hypothesis-testing (Helstrom) detection for binary quantum modulation schemes. Our analysis focuses on the transmission of classical data modulated by quantum coherent states over a log-normal turbulent channel. Additionally, we discuss the lower bounds of the average capacities for Helstrom detection, providing comprehensive insights into the achievable information rates in realistic atmospheric conditions. The derived expressions show excellent agreement with numerical Monte Carlo simulations across a broad range of average transmitted photon numbers, offering valuable guidelines for the design and optimization of quantum communication systems.