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We study the problem of designing optical receivers to discriminate betweenmultiple coherent states using coherent processing receivers---i.e., one thatuses arbitrary coherent feedback control and quantum-noise-limited directdetection---which was shown by Dolinar to achieve the minimum error probabilityin discriminating any two coherent states. We first derive and re-interpretDolinar's binary-hypothesis minimum-probability-of-error receiver as the onethat optimizes the information efficiency at each time instant, based onrecursive Bayesian updates within the receiver. Using this viewpoint, wepropose a natural generalization of Dolinar's receiver design to discriminate$M$ coherent states each of which could now be a codeword, i.e., a sequence of$N$ coherent states each drawn from a modulation alphabet. We analyze thechannel capacity of the pure-loss optical channel with a generalcoherent-processing receiver in the low-photon number regime and compare itwith the capacity achievable with direct detection and the Holevo limit(achieving the latter would require a quantum joint-detection receiver). Weshow compelling evidence that despite the optimal performance of Dolinar'sreceiver for the binary coherent-state hypothesis test (either in errorprobability or mutual information), the asymptotic communication rateachievable by such a coherent-processing receiver is only as good as directdetection. This suggests that in the infinitely-long codeword limit, allpotential benefits of coherent processing at the receiver can be obtained bydesigning a good code and direct detection, with no feedback within thereceiver.

On capacity of optical communications over a lossy bosonic channel with a receiver employing the most general coherent electro-optic feedback control