Quantum measurement and the transformation from quantum to classical probabilities

A specific model of quantum measurement [D. F. Walls, M. J. Collet, and G. J. Milburn, Phys. Rev. D 32, 3208 (1985)] based on a generic system-meter-environment measurement scheme is investigated in terms of probability distributions on projective Hilbert space. Starting from the unitary evolution of the total system a stochastic process for the wave function of the reduced system-meter system is derived by elimination of the degrees of freedom of the environment. The stochastic process is interpreted in terms of the direct detection of the photoelectrons created by the meter quanta in the environment. Two general variances are introduced which represent, respectively, the average intrinsic quantum fluctuations and the statistical fluctuations of the quantum expectation of the measured observable. Involving fourth moments of the wave function, these variances allow to monitor the transformation from quantum to classical probabilities during the process of measurement. copyright 1996 The American Physical Society