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Physical Review A

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

H. Fearn, Willis E. Lamb

Published Sep 1, 1993• 6 citations
Publisher

Abstract

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.
DOI
10.1103/physreva.48.2505

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

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Off-resonant quantum Zeno and anti-Zeno effects on entanglement

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Comment on: “Defense of ‘Impossibility of distant indirect measurement of the quantum Zeno effect’ ” [Phys. Lett. A 356 (2006) 411]

Sascha Wallentowitz, P. E. Toschek

Physics Letters A•Mar 21, 2007•3 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.
We examine the appearance of Zeno and anti-Zeno effects (Misra and Sudarshan 1977 J. Math. Phys. 18 756; Kofman and Kurizki 2000 Nature 405 546; Kofman and Kurizki 1996 Phys. Rev. A 54 3750; Facchi et al 2001 Phys. Rev. Lett. 86 2699) in the entanglement dynamics of two qubits off-resonantly coupled to the same lossy cavity when the unitary evolution of the system is interrupted by repeated projective measurements. We describe in detail these quantum effects by comparing the measurement-induced coarse-grained dynamics to the entanglement evolution in the absence of measurements in several scenarios (Francica et al 2009 Phys. Rev. A 79 032310). In particular, we examine the strong and weak coupling regimes, the role of the relative coupling strengths between the two qubits and the reservoir and the effect of the detuning from the main cavity frequency. We show that the anti-Zeno effect can occur in the entanglement dynamics when the qubit frequencies are detuned from the main reservoir frequency. Furthermore, we find that Zeno and anti-Zeno effects can even appear sequentially many times as a function of the interval between the measurements. Finally, we show that, in the off-resonant regime, we can preserve the entanglement using the quantum Zeno effect more efficiently than in the resonant limit (Maniscalco et al 2008 Phys. Rev. Lett. 100 090503), even if, in this case, no sub-radiant state exists.