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arXiv:quant-ph/0509098 · Physical Review A

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

Sascha Wallentowitz, P. E. Toschek

Published Oct 5, 2005• 10 citations
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Abstract

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.
DOI
10.1103/physreva.72.046101

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Received 15 October 2004DOI:https://doi.org/10.1103/PhysRevA.70.059903©2004 American Physical Society

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We critically study the possibility of the quantum Zeno effect for indirect measurements. If the detector is prepared to detect the emitted signal from the core system, and does not reflect this signal back to the core system, then we can prove that the decay probability of the system is not changed by the continuous measurement of the signal and the quantum Zeno effect would never take place. This argument also applies to the quantum Zeno effect for accelerated two-level systems and unstable particle decays.
We study the quantum Zeno effect in the case of indirect measurement, where the detector does not interact directly with the unstable system. Expanding on the model of Koshino and Shimizu [Phys. Rev. Lett. 92, 030401 (2004)] we consider a realistic Hamiltonian for the detector with a finite bandwidth. We also take explicitly into account the position, the dimensions, and the uncertainty in the measurement of the detector. Our results show that the quantum Zeno effect is not expected to occur, except for the unphysical case where the detector and the unstable system overlap.