Performance measures of quantum-phase measurement

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Abstract
Dispersion and peak likelihood—two performance measures recently used for the description of quantum phase—are compared in this Rapid Communication. The Susskind-Glogower phase operator represents the extremal quantum estimator with respect to both measures. The states with infinite peak likelihood and zero phase information explicitly demonstrate that peak likelihood is not relevant to the phase measurement, whereas dispersion represents a well-behaved performance measure of the phase variable. Peak likelihood restricts the lower limit of the variance of photon number, and the above-mentioned states represent the extremal states of the Shapiro-Shepard [Phys. Rev. A 43, 3795 (1991)] uncertainty relation.

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