Optimum phase-shift estimation and the quantum description of the phase difference

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The problem of a correct quantum description of the phase difference is examined from the perspective of parameter estimation theory. It is shown that an optimum phase-shift measurement defines a phase difference operator which coincides with other approaches to the same problem. We also study the fundamental limit to the accuracy of a phase difference shift detection. We show that this limit can be reached by a measurement having countable outcomes despite the fact that a phase shift can take any value. We show that this is the case of the phase difference operator defined by an optimum phase-shift measurement.
© 1996 The American Physical Society. A.L. acknowledges the support of a grant from the Dirección General de Investigación Científica y Técnica del Ministerio Español de Educación y Ciencia and the kind hospitality from the Optics Department of the Palacký University.
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