Belief propagation with quantum messages for quantum-enhanced classical communications

Abstract For space-based laser communications, when the mean photon number per received optical pulse is much smaller than one, there a large gap between communications capacity achievable with receiver that performs individual pulse-by-pulse detection, and quantum-optimal “joint-detection receiver” acts collectively on long codeword-blocks of modulated pulses; an effect often termed “superadditive capacity”. In this paper, we consider simplest scenario where superadditive known: pure-loss channel coherent-state binary phase-shift keyed (BPSK) modulation. The two BPSK states can be mapped conceptually to non-orthogonal qubit, described by inner product function pulse. Using map, derive explicit construction quantum circuit joint-detection based recent idea “belief-propagation messages” (BPQM). We quantify its performance improvement over Dolinar optimal which represents best “classical” approach. analyze scheme rigorously show it achieves limit minimum average error probability in discriminating 8 codewords length-5 linear code tree factor graph. Our result suggests BPQM might attain Holevo BPSK-modulated channel. Moreover, our provides alternative proposal for supremacy experiment, targeted at specific application potentially implemented small, special-purpose, photonic computer capable performing cat-basis universal qubit logic.