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IEEE Wireless Communications Letters

Quantum Advantage of Binary Discrete Modulations for Space Channels

M. A. Vázquez‐Castro, Bunyod Samandarov

Published Mar 16, 2023• 18 citations
Publisher

Abstract

We assume information is discrete-modulated over coherent states of the single-mode electromagnetic field and transmitted over space quantum channels. In this letter, we provide a comparison of quantum detection with classical detection for communication using on-off keying (OOK) and binary phase shift keying (BPSK) for illustrative system parameters for LEO, MEO and GEO satellites. To do so, we assume an attenuation-only (pure-loss) channel and compute the Shannon capacities for the following detection methods: classical (shot-noise limited) single-photon and coherent detectors as well as optimal quantum hypothesis-testing (Helstrom) detection. As in classical system engineering design, we also obtain theoretical references for comparison, namely, Shannon capacities and Holevo bounds for the ideal Gaussian optical channel. Our results show the ranges of transmitted power and orbital heights for which either classical or quantum detection is optimal, thus providing useful insights into design guidelines and operations of future space communication systems. We also obtain the remarkable result that the BPSK Holevo bound achieves the ultimate quantum capacity of the considered channel.

DOI
10.1109/lwc.2023.3249282

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Quantum Detection and Channel Capacity Using

State-Space Optimization

The fundamental performance limits and channel capacity of optical communications systems operating over the free-space channel will be examined using quantum detection theory. The performance of the optimum quantum receiver for on{ofi keying and optical binary phase-shift keying is flrst examined as a pure-state (no-noise) problem. The classical capacity of the binary symmetric channel for these two modulation schemes will be evaluated for the optimum quantum receiver by making use of the concept of quantum measurement states. The performance of M-ary pulse-position modulation, which requires a product state representation, will be evaluated along with the performance of certain dense signal sets. Performance comparisons with classical techniques show an improvement of over 5 dB in some cases when quantum detection is employed. As a further application of the quantum detection theory, the capacity of the binary channel with on{ofi keyed modulation and quantum detection is evaluated and shown to exceed the capacity obtained with classical photon counting.

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We assume information is discrete-modulated over coherent states of the single-mode electromagnetic field and transmitted over space quantum channels. In this letter, we provide a comparison of quantum detection with classical detection for communication using on-off keying (OOK) and binary phase shift keying (BPSK) for illustrative system parameters for LEO, MEO and GEO satellites. To do so, we assume an attenuation-only (pure-loss) channel and compute the Shannon capacities for the following detection methods: classical (shot-noise limited) single-photon and coherent detectors as well as optimal quantum hypothesis-testing (Helstrom) detection. As in classical system engineering design, we also obtain theoretical references for comparison, namely, Shannon capacities and Holevo bounds for the ideal Gaussian optical channel. Our results show the ranges of transmitted power and orbital heights for which either classical or quantum detection is optimal, thus providing useful insights into design guidelines and operations of future space communication systems. We also obtain the remarkable result that the BPSK Holevo bound achieves the ultimate quantum capacity of the considered channel.
The fundamental performance limits and channel capacity of optical communications systems operating over the free space channel will be examined using quantum detection theory. The performance of the optimum quantum receiver for on-off keying (OOK) and optical binary phase shift keying (BPSK) is first examined as a pure state (no noise) problem. The classical capacity of the binary symmetric channel for these two modulation schemes is then evaluated for the optimum quantum receiver by making use of the concept of quantum measurement states. The performance of M-ary pulse position modulation, which requires a product state representation, is evaluated along with the performance of certain 'dense signal sets.' Performance comparisons with classical techniques shows over 5 dB improvement in some cases when quantum detection is employed. As a further application of the quantum detection theory, the capacity of the binary channel with on-off keyed modulation and quantum detection is evaluated, and shown to exceed the capacity obtained with classical photon counting.
For space-based laser communications, when the mean photon number per received optical pulse is much smaller than one, there is a large gap between communications capacity---measured in bits communicated per pulse---achievable with a receiver that detects (converts from optical to electrical domain) each modulated pulse one at a time, versus with the quantum-optimal joint-detection receiver that acts on a long codeword comprised of nnn modulated pulses; an effect often termed superadditive capacity. The action of this receiver cannot be described as the detection of each individual pulse, interspersed with classical feedforward and soft-information post-processing. In this paper, we consider the simplest scenario where a large superadditive capacity is known: a pure-loss channel with a coherent-state binary phase-shift keyed (BPSK) modulation. The two BPSK states can be mapped conceptually to two non-orthogonal states of a single qubit, described by an inner product that is a function of the mean photon number of each BPSK pulse. Using this map, we derive an explicit construction of the quantum circuit of a joint-detection receiver based on a recent idea of belief-propagation with quantum messages (BPQM) [arXiv:1607.04833]. We analyze this scheme rigorously and show that it achieves the quantum limit of minimum average error probability in discriminating 888 (BPSK) codewords of a length-555 binary linear code with a tree factor graph. We quantify its performance improvement over the (Dolinar) receiver that optimally detects one pulse at a time. Our result suggests that a BPQM-receiver might attain the Holevo capacity, the quantum limit of classical communication capacity, of this BPSK-modulated pure-loss channel. This suggests a new application for a small, special-purpose, photonic quantum computer capable of so-called cat-basis universal qubit logic.
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.
With the increasing demand for secure communication in optical space networks, it is essential to develop physical-layer scalable security solutions. In this context, we present the asymptotic security analysis of a keyless quantum private communication protocol that transmits classical information over quantum states. Different from the previous literature, our protocol sends dummy (decoy) states optimally obtained from the true information to deceive the eavesdropper. We analyze optical on-off keying (OOK) and binary phase shift keying (BPSK) for several detection scenarios. Our protocol significantly improves the protocol without decoy states whenever Bob is at a technological disadvantage with respect to Eve. Our protocol guarantees positive secrecy capacity when the eavesdropper gathers up to 90-99.9% (depending on the detection scenario) of the photon energy that Bob detects, even when Eve is only limited by the laws of quantum mechanics. We apply our results to the design of an optical inter-satellite link (ISL) study case with pointing losses, and introduce a new design methodology whereby the link margin is guaranteed to be secure by our protocol. Hence, our design does not require knowing the eavesdropper’s location and/or channel state: the protocol aborts whenever the channel drops below the secured margin. Our protocol can be implemented with state-of-the-art space-proof technology. Finally, we also show the potential secrecy advantage when using (not yet available) squeezed quantum states technology.
Abstract For space-based laser communications, when the mean photon number per received optical pulse is much smaller than one, there is a large gap between communications capacity achievable with a receiver that performs individual pulse-by-pulse detection, and the quantum-optimal “joint-detection receiver” that acts collectively on long codeword-blocks of modulated pulses; an effect often termed “superadditive capacity”. In this paper, we consider the simplest scenario where a large superadditive capacity is known: a pure-loss channel with a coherent-state binary phase-shift keyed (BPSK) modulation. The two BPSK states can be mapped conceptually to two non-orthogonal states of a qubit, described by an inner product that is a function of the mean photon number per pulse. Using this map, we derive an explicit construction of the quantum circuit of a joint-detection receiver based on a recent idea of “belief-propagation with quantum messages” (BPQM). We quantify its performance improvement over the Dolinar receiver that performs optimal pulse-by-pulse detection, which represents the best “classical” approach. We analyze the scheme rigorously and show that it achieves the quantum limit of minimum average error probability in discriminating 8 (BPSK) codewords of a length-5 binary linear code with a tree factor graph. Our result suggests that a BPQM receiver might attain the Holevo capacity of this BPSK-modulated pure-loss channel. Moreover, our receiver circuit provides an alternative proposal for a quantum supremacy experiment, targeted at a specific application that can potentially be implemented on a small, special-purpose, photonic quantum computer capable of performing cat-basis universal qubit logic.
The fundamental performance limits and channel capacity of optical communications systems operating over the free-space channel will be examined using quantum detection theory. The performance of the optimum quantum receiver for on{ofi keying and optical binary phase-shift keying is flrst examined as a pure-state (no-noise) problem. The classical capacity of the binary symmetric channel for these two modulation schemes will be evaluated for the optimum quantum receiver by making use of the concept of quantum measurement states. The performance of M-ary pulse-position modulation, which requires a product state representation, will be evaluated along with the performance of certain dense signal sets. Performance comparisons with classical techniques show an improvement of over 5 dB in some cases when quantum detection is employed. As a further application of the quantum detection theory, the capacity of the binary channel with on{ofi keyed modulation and quantum detection is evaluated and shown to exceed the capacity obtained with classical photon counting.