OPTIMUM PHASE-SHIFT ESTIMATION AND THE QUANTUM DESCRIPTION OF THE PHASE DIFFERENCE

The problem of a correct quantum description of the phase difference i s examined from the perspective of parameter estimation theory. It is shown that an optimum phase-shift measurement defines a phase differen ce operator which coincides with other approaches to the same problem. We also study the fundamental limit to the accuracy of a phase differ ence shift detection. We show that this limit can be reached by a meas urement having countable outcomes despite the fact that a phase shift can take any value. We show that this is the case of the phase differe nce operator defined by an optimum phase-shift measurement.