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Physical Review A

Comment on ‘‘Intrinsic decoherence in quantum mechanics’’

J. Finkelstein

Published Mar 1, 1993• 11 citations
Publisher

Abstract

Milburn has recently proposed a model [Phys. Rev. A 44, 5401 (1991)] in which quantum states evolve into statistical mixtures of stationary states. One might think that this would imply that any observable quantity would become independent of time. We argue that, on the contrary, the decoherence implied by Milburn's model would have no observable effect at all.

DOI
10.1103/physreva.47.2412

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Reply to ‘‘Comment on ‘Intrinsic decoherence in quantum mechanics’ ’’

Gerard J Milburn

Finkelstein’s criticism [Phys. Rev. A (to be published)] of my paper [Phys. Rev. A 44, 5401 (1991)] presupposes time measurements of an accuracy explicitly ruled out in the paper.Received 7 July 1992DOI:https://doi.org/10.1103/PhysRevA.47.2415©1993 American Physical Society

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We analyze the time evolution of entanglement of two-qutrit system within the framework of Milburn's model of intrinsic decoherence. The entanglement evolution relies not only on the parameters of system, but also on the concrete states either pure or mixed. The linear entropy used to measure the extent to which the intrinsic decoherence affects quantum states is evaluated.

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Reply to ‘‘Comment on ‘Why quantum mechanics cannot be formulated as a Markov process’’’

Daniel T. Gillespie

In reply to the preceding Comment on an article by D. T. Gillespie [Phys. Rev. A 49, 1607 (1994)], it is emphasized that the most plausible interpretation of the singly conditioned probability function implies that the evolution of the two-state quantum system being considered cannot be characterized as a Markov process on those states over any time interval. And it is pointed out that an alternative interpretation that is offered in the Comment appears to be in conflict with quantum mechanics.

Physical Review A•Aug 1, 1996•5 citations
Milburn has recently proposed a model [Phys. Rev. A 44, 5401 (1991)] in which quantum states evolve into statistical mixtures of stationary states. One might think that this would imply that any observable quantity would become independent of time. We argue that, on the contrary, the decoherence implied by Milburn's model would have no observable effect at all.
Milburn has recently proposed [Phys. Rev. A 44, 5401 (1991)] a variation of the Schr\"odinger equation which models decoherence as the system evolves through intrinsic mechanisms beyond conventional quantum mechanics rather than dissipative interaction with an environment. In this paper we give an exact solution of this equation and apply it to the Jaynes-Cummings model of atom-field interaction with nontrivial dynamics. We show that the intrinsic decoherence is responsible for deterioration of quantum coherence effects in this model, such as revivals of the atomic inversion. We discuss the applicability of the Milburn equation.
The discrete-time jump model for intrinsic decoherence in quantum mechanics proposed recently by Milburn is here generalized to explicitly time-dependent Hamiltonians. In this model, a time-dependent entropy is obtained and thus it admits of an interpretation that this is a model for an open system. Unlike in the Milburn model, we introduce a minimum uncertainty phase change dictated by the minimum ``time-energy uncertainty product'' to define the shortest time scale in the system. Implications of this model to quantum nanometric devices such as quantum dots or resonant tunneling devices are indicated. \textcopyright{} 1996 The American Physical Society.