Capacity of coherent-state adaptive decoders with interferometry and single-mode detectors

A class of adaptive decoders (ADs) for coherent-state sequences is studied, including in particular the most common technology for optical-signal processing, e.g., interferometers, coherent displacements, and photon-counting detectors. More generally we consider ADs comprising adaptive procedures based on passive multimode Gaussian unitaries and arbitrary single-mode destructive measurements. For classical communication on quantum phase-insensitive Gaussian channels with a coherent-state encoding, we show that the AD's optimal information transmission rate is not greater than that of a single-mode decoder. Our result also implies that the ultimate classical capacity of quantum phase-insensitive Gaussian channels is unlikely to be achieved with the considered class of ADs.