  After a derivation of the quantum Bayes theorem, and a discussion of the
reconstruction of the unknown state of identical spin systems by repeated
measurements, the main part of this paper treats the problem of determining the
unknown phase difference of two coherent sources by photon measurements. While
the approach of this paper is based on computing correlations of actual
measurements (photon detections), it is possible to derive indirectly a
probability distribution for the phase difference. In this approach, the
quantum phase is not an observable, but a parameter of an unknown quantum
state. Photon measurements determine a probability distribution for the phase
difference. The approach used in this paper takes into account both photon
statistics and the finite efficiency of the detectors.
