Quantum phase detection and digital communication

A canonical description of electromagnetic phase, related to both the Susskind-Glogower and Pegg-Barnett phase formalisms is applied to determine the quantum limits for digital communication based on phase detection. It is proved that canonical phase detection is superior to all other shift-invariant phase detection methods, in its ability to accurately resolve signals into phase bins under any given energy constraint. Under a bounded energy constraint, the optimal signal states are characterized in terms of discrete prolate spheroidal sequences and an asymptotic formula is given for the minimum error rate. Numerical results are given to provide comparison between canonical and heterodyne phase detection. A new method of deriving the statistics of (ideal) heterodyne detection for a given image-band field is presented.

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