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Physical Review A

Comment on ‘‘Computational approach to the quantum Zeno effect: Position measurements’’

Dipankar Home, M. A. B. Whitaker

Published Sep 1, 1993• 10 citations
Publisher

Abstract

We examine results presented by Fearn and Lamb [Phys. Rev. A 46, 1199 (1992)], who search for, but fail to find, the quantum Zeno effect in measurements of the position of a particle in a double potential well, and criticize the basic statement of the effect given by Misra and Sudarshan [J. Math. Phys. 18, 756 (1977)]. We suggest that position measurements are an inappropriate area to look for the effect; nevertheless, we show that some of the results of Fearn and Lamb should, and do, exhibit a form of weak effect. Though the collapse postulate, as used by Misra and Sudarshan, is not required to discuss quantum measurement and the quantum Zeno effect, its application describes adequately the results of measurement, and we reject the idea that the basic statement of the quantum Zeno effect is flawed.

DOI
10.1103/physreva.48.2502

Related papers

Reply to ‘‘Comment on ‘Computational approach to the quantum Zeno effect: Position measurements’ ’’

H. Fearn, Willis E. Lamb

This is a Reply to the preceding Comment by Home and Whitaker [Phys. Rev. A 48, 2502 (1993)]. Our aim is to indicate how we apply basic quantum mechanics to quantum measurement theory. We discuss the work of Misra and Sudarshan [J. Math. Phys. 18, 576 (1977)] and defend our own work on the quantum Zeno effect.

Physical Review A•Sep 1, 1993•6 citations

Reply to ‘‘Comment on ‘Quantum Zeno effect’’’

Wayne M. Itano, Daniel J. Heinzen, J. J. Bollinger +1 more

Various interpretations of quantum mechanics are valid insofar as they predict the same experimental results. Some invoke ``wave-function collapse'' and some do not. An interpretation based on the collapse postulate provides a simple explanation for a recent experimental demonstration of the quantum Zeno effect [Itano et al., Phys. Rev. A 41, 2295 (1990)], but other interpretations are also valid.

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Simple computer model for the quantum Zeno effect

David Wallace

This paper presents a simple model for repeated measurement of a quantum system: the evolution of a free particle, simulated by discretizing the particle's position. This model is easily simulated by computer and provides a useful arena to investigate the effects of measurement upon dynamics, in particular the slowing of evolution due to measurement (the quantum Zeno effect). The results of this simulation are discussed for two rather different sorts of measurement process, both of which are (simplified forms of) measurements used in previous simulations of position measurement. A number of interesting results due to measurement are found, and the investigation casts some light on previous disagreements about the presence or absence of the Zeno effect.

arXiv:quant-ph/0004011•Physical Review A•Jan 17, 2001•8 citations

Comment on “Impossibility of distant indirect measurement of the quantum Zeno effect”

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In the paper by M. Hotta and M. Morikawa [Phys. Rev. A 69, 052114 (2004)] the non-existence of the quantum Zeno effect caused by indirect measurements has been claimed. It is shown here that the pertinent proof is incorrect, and the claim unfounded.

arXiv:quant-ph/0509098•Physical Review A•Oct 5, 2005•10 citations

Computational approach to the quantum Zeno effect: Position measurements

H. Fearn, Willis E. Lamb

We present computational results of quantum-mechanical sequential measurements of a single dynamical variable (position) in a barrier penetration system. Our model is based on a well-rounded two-minima potential with a particle initially located on one side of the barrier. First we allow the particle wave function to propagate without further disturbance and calculate its barrier penetration time, then we perform measurements of the particle's position and contrast the barrier penetration time T with the results for the undisturbed system. The time-dependent Schr\"odinger equation for the problem was solved using fast-Fourier-transform techniques. The barrier penetration time was found to depend on (1) the type of measurement made, (2) the strength of the interaction of the system with the meter, (3) the rate at which the measurements were performed, and (4) the precision of the meter (which in our model is related to the width of the meter's wave function). We find no evidence in support of the Zeno effect. However, by using a caricature of quantum mechanics we can obtain results similar to the Zeno effect.

Physical Review A•Aug 1, 1992•39 citations

Understanding the quantum Zeno effect

Hiromichi Nakazato, Mikio Namiki, Saverio Pascazio +1 more

The quantum Zeno effect consists in the hindrance of the evolution of a quantum system that is very frequently monitored and found to be in its initial state at every single measurement. On the basis of the correct formula for the survival probability, i.e. the probability of finding the system in its initial state at every single measurement, we critically analyze a recent proposal and experimental test, that make use of an oscillating system. PACS: 03.65.Bz, 42.50.-p 1 The seminal formulation of the quantum Zeno effect, due to Misra and Sudarshan [1], deals with the probability of observing an unstable system in its initial state throughout a time interval ∆ = [0, t]. The purpose of this note is to point out that the quantum Zeno effect has not been experimentally observed, yet, in its original formulation. Indeed, we shall argue that the interesting proposal by Cook [2], that makes use of a two-level system undergoing Rabi oscillations, as well as the beautiful experiment performed by Itano et al. [3], investigate the probability of finding the

•Jan 1, 1996•36 citations
We examine results presented by Fearn and Lamb [Phys. Rev. A 46, 1199 (1992)], who search for, but fail to find, the quantum Zeno effect in measurements of the position of a particle in a double potential well, and criticize the basic statement of the effect given by Misra and Sudarshan [J. Math. Phys. 18, 756 (1977)]. We suggest that position measurements are an inappropriate area to look for the effect; nevertheless, we show that some of the results of Fearn and Lamb should, and do, exhibit a form of weak effect. Though the collapse postulate, as used by Misra and Sudarshan, is not required to discuss quantum measurement and the quantum Zeno effect, its application describes adequately the results of measurement, and we reject the idea that the basic statement of the quantum Zeno effect is flawed.
This paper presents a simple model for repeated measurement of a quantum system: the evolution of a free particle, simulated by discretizing the particle's position. This model is easily simulated by computer and provides a useful arena to investigate the effects of measurement upon dynamics, in particular the slowing of evolution due to measurement (the quantum Zeno effect). The results of this simulation are discussed for two rather different sorts of measurement process, both of which are (simplified forms of) measurements used in previous simulations of position measurement. A number of interesting results due to measurement are found, and the investigation casts some light on previous disagreements about the presence or absence of the Zeno effect.
We present computational results of quantum-mechanical sequential measurements of a single dynamical variable (position) in a barrier penetration system. Our model is based on a well-rounded two-minima potential with a particle initially located on one side of the barrier. First we allow the particle wave function to propagate without further disturbance and calculate its barrier penetration time, then we perform measurements of the particle's position and contrast the barrier penetration time T with the results for the undisturbed system. The time-dependent Schr\"odinger equation for the problem was solved using fast-Fourier-transform techniques. The barrier penetration time was found to depend on (1) the type of measurement made, (2) the strength of the interaction of the system with the meter, (3) the rate at which the measurements were performed, and (4) the precision of the meter (which in our model is related to the width of the meter's wave function). We find no evidence in support of the Zeno effect. However, by using a caricature of quantum mechanics we can obtain results similar to the Zeno effect.
The quantum Zeno effect consists in the hindrance of the evolution of a quantum system that is very frequently monitored and found to be in its initial state at every single measurement. On the basis of the correct formula for the survival probability, i.e. the probability of finding the system in its initial state at every single measurement, we critically analyze a recent proposal and experimental test, that make use of an oscillating system. PACS: 03.65.Bz, 42.50.-p 1 The seminal formulation of the quantum Zeno effect, due to Misra and Sudarshan [1], deals with the probability of observing an unstable system in its initial state throughout a time interval ∆ = [0, t]. The purpose of this note is to point out that the quantum Zeno effect has not been experimentally observed, yet, in its original formulation. Indeed, we shall argue that the interesting proposal by Cook [2], that makes use of a two-level system undergoing Rabi oscillations, as well as the beautiful experiment performed by Itano et al. [3], investigate the probability of finding the