Quantum photonic communications with four-dimensional constellations of coherent states undergoing phase noise

Abstract

We present the analysis of the quantum detection of modulated coherent states used in quantum communications systems that employ the degrees of freedom of both the complex amplitude and the state of polarization of the optical carrier, in the presence of optical phase fluctuations, unavoidable in realistic laser fields as optical sources in photonic communications.

We analyze several photonic M-ary constellations with different four-dimensional (4D) formats with joint modulation of the field quadratures and the states of polarization of quantum coherent states affected by optical phase noise, of interest in quantum photonic communications, cryptography, and other applications.

For the quantum state detection/discrimination at the receiver, we employ the square root method (SRM) for the received phase-diffused 4D constellations, constituted by a set of mixed quantum coherent states, and arrive at results on their performance in error probability, as well as their mutual information, spectral and photon number efficiencies.

We find that the overall performances of our 4D Polarization-Shifted and Polarization-Multiplexed constellations are better than those of their single polarization counterparts; also, our binary and quaternary Phase-Shift-Keying formats perform better than the On-Off-Keying and Pulse-Position-Modulation schemes, with a trade-off with their sensitivity to phase noise, which is quantified in our analysis.