Testing of quantum phase in matter-wave optics

Various phase concepts may be treated as special cases of the maximum likel ihood estimation. For example, the discrete Fourier estimation that actuall y coincides with the operational phase of Noh, Fougeres, and Mandel is obta ined for continuous Gaussian signals with phase modulated mean. Since signa ls in quantum theory are discrete, a prediction different from that given b y the Gaussian hypothesis should be obtained as the best fit assuming a dis crete Poissonian statistics of the signal. Although the Gaussian estimation gives a satisfactory approximation for fitting the phase distribution of a lmost any state, the optimal phase estimation offers in certain cases a mea surably better performance. This has been demonstrated in a neutron-optical experiment. [S1050-2947(99)02307-0].