Quantum Nondemolition Measurements and the “Collapse” of the Wave Function

Michel Bauer, Denis Bernard

Michel Bauer, Denis Bernard

Motivated by recent experiments on quantum trapped fields, we give a rigorous proof that repeated indirect quantum nondemolition (QND) measurements converge to the collapse of the wave function as predicted by the postulates of quantum mechanics for direct measurements. We also relate the rate of convergence toward the collapsed wave function to the relative entropy of each indirect measurement, a result which makes contact with information theory.

Gerard J Milburn, Daniel F. Walls

Orly Alter, Y. Yamamoto

It is shown that a series of repeated weak quantum nondemolition measurements performed on a single quantum system gives no information about the wave function of the system. The physical explanation, based on the quantum Brownian motion and the continuous collapse of the wave function which originate in the projection postulate, is discussed in two specific examples.

Александр Семенович Холево

Franz X. Kärtner, H. A. Haus

This paper intends to clarify some issues in the theory of quantum measurement by taking advantage of the self-consistent quantum formulation of nonlinear optics. A quantum-nondemolition measurement of the photon number of an optical pulse can be performed with a nonlinear Mach-Zehnder interferometer followed by a balanced detector. The full quantum-mechanical treatment shows that the shortcut in the description of the quantum-mechanical measurement, the so-called ``collapse of the wave function,'' is not needed for a self-consistent interpretation of the measurement process. Coherence in the density matrix of the signal to 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 information on the photon number in one of the two paths. The ``gain'' in the measurement can be made arbitrarily large so that postprocessing of the information can proceed classically.