  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.
