Luis Aina, AlfredoPeřina, J.2023-06-202023-06-201996-111050-294710.1103/PhysRevA.54.4564https://hdl.handle.net/20.500.14352/59726© 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.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.engjournal articlehttp://dx.doi.org/10.1103/PhysRevA.54.4564http://journals.aps.org/open access535Optical-phaseOperatorUncertaintyStatesLightÓptica (Física)2209.19 Óptica Física