Detection of polarization shift-keyed/switched/multiplexed quantum coherent states in M-ary photonic communication systems

In this work, we present the analysis of the quantum detection of information-carrying coherent states used in optical communications systems that employ the degrees of freedom of both the complex amplitude and the state of polarization of the laser field. In these quantum communication systems, the transmitter prepares a set of quantum states (a constellation of quantum composite coherent states) producing a four-dimensional (4D) M-ary modulation, that is sent through the optical channel, in diverse formats such as: a) polarization shift-keying (PolSK), b) polarization switching (PS), or c) polarization multiplexing (PM). At the receiver, measurements are performed to determine as accurately as possible which state was sent, with a discrimination method aided by any prior information. With this purpose, in this work we apply the square root method (SRM) for the received composite quantum state constellations and study their performance in error probability and mutual information for several 4D M-ary coherent state modulation formats, inspired by constellations commonly used in classical photonic communications. We arrive at closed form expressions both for the error probability and for the mutual information, for most of the modulation formats analyzed.