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arXiv:1706.09676

Inhibition of Purification Processes through Zeno effect

Benedetto Militello, Anna Napoli

Published Jun 29, 2017• 0 citations
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Abstract

It is shown that a generalized quantum Zeno effect based on the introduction of a coherent coupling between several parts of a compound system can be responsible for neutralizing the effects of repeated measurements. To demonstrate this effect, we focus on a purification scheme based on iterated observations on an ancilla system put in interaction with the main one [Nakazato, Takazawa, Yuasa, Phys. Rev. Lett. {\bf 90}, 060401 (2003)]. We bring to light that a suitable Hilbert space partitioning due to an appropriate interaction can eliminate the effects of repeated wave function collapses the purification scheme is based on.

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Comment on ‘‘Quantum Zeno effect’’

L. E. Ballentine

The quantum Zeno effect is not a general characteristic of continuous measurements. In a recently reported experiment [Itano et al., Phys. Rev. A 41, 2295 (1990)], the inhibition of atomic excitation and deexcitation is not due to any ``collapse of the wave function,'' but instead is caused by a very strong perturbation due to the optical pulses and the coupling to the radiation field. The experiment should not be cited as providing empirical evidence in favor of the notion of ``wave-function collapse.''

Physical Review A•May 1, 1991•84 citations
It is shown that a generalized quantum Zeno effect based on the introduction of a coherent coupling between several parts of a compound system can be responsible for neutralizing the effects of repeated measurements. To demonstrate this effect, we focus on a purification scheme based on iterated observations on an ancilla system put in interaction with the main one [Nakazato, Takazawa, Yuasa, Phys. Rev. Lett. {\bf 90}, 060401 (2003)]. We bring to light that a suitable Hilbert space partitioning due to an appropriate interaction can eliminate the effects of repeated wave function collapses the purification scheme is based on.
A method of purification through Zeno-like measurements has been proposed by Nakazato and co-workers [H. Nakazato, T. Takazawa, and K. Yuasa, Phys. Rev. Lett. 90, 060401 (2003); H. Nakazato, M. Unoki, and K. Yuasa, Phys. Rev. A 70, 012303 (2004)]. A series of frequent measurements on a quantum system is demonstrated to result in the purification of another quantum system in interaction with the former. Inspired by this idea, we have designed a strategy to obtain entangled states through only two measurements. A deterministic purification method is also provided in this article.
A method of purification, purification through Zeno-like measurements [H. Nakazato, T. Takazawa, and K. Yuasa, Phys. Rev. Lett. 90, 060401 (2003)], is discussed extensively and applied to a few simple qubit systems. It is explicitly demonstrated how it works and how it is optimized. As possible applications, schemes for initialization of multiple qubits and entanglement purification are presented, and their efficiency is investigated in detail. Simplicity and flexibility of the idea allow us to apply it to various kinds of settings in quantum information and computation, and would provide us with useful and practical methods of state preparation.
Itano and co-workers [Wayne M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, Phys. Rev. A 41, 2295 (1990)] have recently reported the experimental verification of the quantum Zeno effect, which is the inhibition of a quantum transition by frequent measurements. In this article, we offer an alternative interpretation of the quantum Zeno effect. We show that an analysis of the dynamics of the full three-level system gives the same result. There is no need to assume explicitly that the wave function has collapsed, nor even to assume that an ideal measurement has been made. In addition, we differentiate between what has been referred to as the quantum Zeno effect and what has been termed the quantum Zeno paradox. The former is the inhibition of induced transitions, and the latter is the, as yet experimentally unobserved, inhibition of spontaneous decay. Our interpretation, which emphasizes the ``measurement''-induced interruption of atomic-state coherences as the cause of inhibited quantum transitions, suggests a resolution to the quantum Zeno paradox. The theoretical limit of continuous observation is discussed.
We present a novel procedure to purify quantum states, i.e., purification through Zeno-like measurements. By simply repeating one and the same measurement on a quantum system, one can purify another system in interaction with the former. The conditions for the (efficient) purification are specified on a rather general setting, and the framework of the method possesses wide applicability. It is explicitly demonstrated on a specific setup that the purification becomes very efficient by tuning relevant parameters.
The quantum Zeno effect is not a general characteristic of continuous measurements. In a recently reported experiment [Itano et al., Phys. Rev. A 41, 2295 (1990)], the inhibition of atomic excitation and deexcitation is not due to any ``collapse of the wave function,'' but instead is caused by a very strong perturbation due to the optical pulses and the coupling to the radiation field. The experiment should not be cited as providing empirical evidence in favor of the notion of ``wave-function collapse.''