Quantum-Message-Passing Receiver for Quantum-Enhanced Classical Communications
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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 n 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 8 (BPSK) codewords of a length-5 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.
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