QUANTUM-NONDEMOLITION MEASUREMENTS AND THE COLLAPSE OF THE WAVE-FUNCTION

This paper intends to clarify some issues in the theory of quantum mea surement by taking advantage of the self-consistent quantum formulatio n of nonlinear optics. A quantum-nondemolition measurement of the phot on number of an optical pulse can be performed with a nonlinear Mach-Z ehnder interferometer followed by a balanced detector. The full quantu m-mechanical treatment shows that the shortcut in the description of t he quantum-mechanical measurement, the so-called ''collapse of the wav e function,'' is not needed for a self-consistent interpretation of th e measurement process. Coherence in the density matrix of the signal t o be measured is progressively reduced with increasing accuracy of the photon-number determination. The quantum-nondemolition measurement is incorporated in the double-slit experiment and the contrast ratio of the fringes is found to decrease systematically with increasing inform ation on the photon number in one of the two paths. The ''gain'' in th e measurement can be made arbitrarily large so that postprocessing of the information can proceed classically.