Modal Dynamics for Positive Operator Measures

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Title Modal Dynamics for Positive Operator Measures
Author Gambetta, Jay; Wiseman, Howard Mark
Journal Name Foundations of Physics
Year Published 2004
Place of publication New York
Publisher Plenum Publishing Corporation
Abstract The modal interpretation of quantum mechanics allows one to keep the standard classical definition of realism intact. That is, variables have a definite status for all time and a measurement only tells us which value it had. However, at present modal dynamics are only applicable to situations that are described in the orthodox theory by projective measures. In this paper we extend modal dynamics to include positive operator measures (POMs). That is, for example, rather than using a complete set of orthogonal projectors, we can use an overcomplete set of nonorthogonal projectors. We derive the conditions under which Bell's stochastic modal dynamics for projective measures reduce to deterministic dynamics, showing (incidentally) that Brown and Hiley's generalization of Bohmian mechanics [quant-ph/0005026, (2000)] cannot be thus derived. We then show how deterministic dynamics for positive operators can also be derived. As a simple case, we consider a Harmonic oscillator, and the overcomplete set of coherent state projectors (i.e., the Husimi POM). We show that the modal dynamics for this POM in the classical limit correspond to the classical dynamics, even for the nonclassical number state |n>. This is in contrast to the Bohmian dynamics, which for energy eigenstates, the dynamics are always non-classical.
Peer Reviewed Yes
Published Yes
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Copyright Statement Copyright 2004 Springer-Verlag. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher.The original publication is available at
Volume 34
Page from 419
Page to 448
ISSN 0015-9018
Date Accessioned 2005-03-08
Language en_AU
Research Centre Centre for Quantum Dynamics
Faculty Faculty of Science
Subject PRE2009-Quantum Optics and Lasers
Publication Type Journal Articles (Refereed Article)
Publication Type Code c1

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