Multi-Phase Hadamard receivers for classical communication on lossy bosonic channels

A scheme for transferring classical information over a lossy bosonic channel is proposed by generalizing the proposal presented in Phys. Rev. Lett. 106, 240502 (2011) by Guha. It employs codewords formed by products of coherent states of fixed mean photon number with multiple phases which, through a passive unitary transformation, reduce to a Pulse-Position Modulation code with multiple pulse phases. The maximum information rate achievable with optimal, yet difficult to implement, detection schemes is computed and shown to saturate the classical capacity of the channel in the low energy regime. An easy to implement receiver based on a conditional Dolinar detection scheme is also proposed finding that, while suboptimal, it allows for improvements in an intermediate photon-number regime with respect to previous proposals.