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Quantum phase communication channels in the presence of static and dynamical phase diffusion

We address quantum communication channels based on phase modulation of coherent states and analyze in details the effects of static and dynamical (stochastic) phase diffusion. We evaluate mutual information for an ideal phase receiver and for a covariant phase-space-based receiver, and compare their performances by varying the number of symbols in the alphabet and/or the overall energy of the channel. Our results show that phase communication channels are generally robust against phase noise, especially for large alphabets in the low energy regime. In the presence of dynamical (non-Markovian) noise the mutual information is preserved by the time correlation of the environment, and when the noise spectra is detuned with respect to the information carrier, revivals of mutual information appears.