Publication Date:
2012-09-27
Description:
We analyze general enough models of repeated indirect measurements in which a quantum system interacts repeatedly with randomly chosen probes on which von Neumann direct measurements are performed. We prove, under suitable hypotheses, that the system state probability distribution converges after a large number of repeated indirect measurements, in a way compatible with quantum wave function collapse. We extend this result to mixed states and we prove similar results for the system density matrix. We show that the convergence is exponential with a rate given by some relevant mean relative entropies. We also prove that, under appropriate rescaling of the system and probe interactions, the state probability distribution and the system density matrix are solutions of stochastic differential equations modeling continuous-time quantum measurements. We analyze the large time behavior of these continuous time processes and prove convergence. Content Type Journal Article Pages 1-41 DOI 10.1007/s00023-012-0204-x Authors Michel Bauer, Institut de Physique Théorique, CEA/DSM/IPhT, Unité de recherche associée au CNRS, Point Courrier 136, CEA-Saclay, 91191 Gif sur Yvette Cedex, France Tristan Benoist, Laboratoire de Physique Théorique de l’ENS, CNRS & École Normale Supérieure de Paris, 24, rue Lhomond, 75005 Paris, France Denis Bernard, Laboratoire de Physique Théorique de l’ENS, CNRS & École Normale Supérieure de Paris, 24, rue Lhomond, 75005 Paris, France Journal Annales Henri Poincare Online ISSN 1424-0661 Print ISSN 1424-0637
Print ISSN:
1424-0637
Electronic ISSN:
1424-0661
Topics:
Mathematics
,
Physics
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