Belief Propagation with Quantum Messages for Quantum-Enhanced Classical Communications

• URL: http://arxiv.org/abs/2003.04356v2
• Date: Fri, 7 May 2021 16:52:12 GMT
• Title: Belief Propagation with Quantum Messages for Quantum-Enhanced Classical Communications
• Authors: Narayanan Rengaswamy, Kaushik P. Seshadreesan, Saikat Guha, Henry D. Pfister
• Abstract summary: In space-based laser communications, 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" We show that a BPQM-receiver might attain the Holevo capacity of this BPSK-modulated pure-loss channel.
• Score: 10.881273953303268
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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) (arXiv:1607.04833). 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.

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