QUANTUM MEASUREMENT AND THE TRANSFORMATION FROM QUANTUM TO CLASSICAL PROBABILITIES

A specific model of quantum measurement [D. F. Walls, M. J. Collet, an d G. J. Milburn, Phys. Rev. D 32, 3208 (1985)] based on a generic syst em-meter-environment measurement scheme is investigated in terms of pr obability distributions on projective Hilbert space. Starting from the unitary evolution of the total system a stochastic process for the wa ve function of the reduced system-meter system is derived by eliminati on of the degrees of freedom of the environment. The stochastic proces s is interpreted in terms of the direct detection of the photoelectron s created by the meter quanta in the environment. Two general variance s are introduced which represent, respectively, the average intrinsic quantum fluctuations and the statistical fluctuations of the quantum e xpectation of the measured observable. Involving fourth moments of the wave function, these variances allow to monitor the transformation fr om quantum to classical probabilities during the process of measuremen t.