Approaching the ultimate limits of communication efficiency with a photon-counting detector

Coherent states achieve the Holevo capacity of a pure-loss channel when paired with an optimal measurement, but a physical realization of this measurement is as of yet unknown, and it is also likely to be of high complexity. In this paper, we focus on the photon-counting measurement and study the photon and dimensional efficiencies attainable with modulations over classical- and nonclassical-state alphabets. We first review the state-of-the-art coherent on-off-keying (OOK) with a photon-counting measurement, illustrating its asymptotic inefficiency relative to the Holevo limit. We show that a commonly made Poisson approximation in thermal noise leads to unbounded photon information efficiencies, violating the conjectured Holevo limit. We analyze two binary-modulation architectures that improve upon the dimensional versus photon efficiency tradeoff achievable with conventional OOK. We show that at high photon efficiency these architectures achieve an efficiency tradeoff that differs from the best possible tradeoff-determined by the Holevo capacity-by only a constant factor. The first architecture we analyze is a coherent-state transmitter that relies on feedback from the receiver to control the transmitted energy. The second architecture uses a single-photon number-state source.