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Zeno or Anti-Zeno : which is more useful?

Gershon Kurizki

Published Jan 1, 2011• 0 citations
Publisher

Abstract

The quantum Zeno effect (QZE) introduced by Misra and Sudarshan consists in the ability of repeated measurements to inhibit or slow down unitary evolution. Its fundamental status in quantum mechanics has long been firmly established, but its much broader context, in-depth understanding and its applications are growing at a faster pace than ever before. Over the years, there have been several pivotal developments that have made the QZE and related effects the basic paradigms underlying the control of evolution in quantum systems:

DOI
10.1364/qels.2011.qthb1

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The quantum Zeno effect (QZE) is the striking prediction that the decay of any unstable quantum state can be inhibited by sufficiently frequent observations (measurements). The consensus opinion has upheld the QZE as a general feature of quantum mechanics, which should lead to the inhibition of any decay. The claim of QZE generality hinges on the assumption that successive observations can in principle be made at time intervals too short for the system to change appreciably. However, this assumption and the generality of the QZE have scarcely been investigated thus far. We have addressed these issues by showing that (i) the QZE is principally unattainable in radiative or radioactive decay, because the required measurement rates would cause the system to disintegrate; (ii) decay acceleration by frequent measurements (the anti-Zeno effect -- AZE) is much more ubiquitous than its inhibition. The AZE is shown to be observable as the enhancement of tunneling rates (e.g., for atoms trapped in ramped-up potentials or in current-swept Josephson junctions), fluorescence rates (e.g., for Rydberg atoms perturbed by noisy optical fields) and photon depolarization rates (in randomly modulated Pockels cells).

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The term 'quantum Zeno paradox' or 'quantum Zeno effect' refers to the slowing down of the evolution of a quantum system as it is observed more and more frequently.In 1977, Misra and Sudarshan gave a theoretical demonstration of its existence.There has been disagreement regarding the definition of the effect and whether it is really a paradox, requiring new physics, or a consequence of ordinary quantum mechanics.The experiment of Itano, Heinzen, Bollinger and Wineland, published in 1990, is the one most often called a demonstration of the quantum Zeno effect.Some different interpretations are discussed.

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The quantum Zeno effect (QZE) introduced by Misra and Sudarshan consists in the ability of repeated measurements to inhibit or slow down unitary evolution. Its fundamental status in quantum mechanics has long been firmly established, but its much broader context, in-depth understanding and its applications are growing at a faster pace than ever before. Over the years, there have been several pivotal developments that have made the QZE and related effects the basic paradigms underlying the control of evolution in quantum systems:
The quantum Zeno effect (QZE) is the striking prediction that the decay of any unstable quantum state can be inhibited by sufficiently frequent observations (measurements). The consensus opinion has upheld the QZE as a general feature of quantum mechanics, which should lead to the inhibition of any decay. The claim of QZE generality hinges on the assumption that successive observations can in principle be made at time intervals too short for the system to change appreciably. However, this assumption and the generality of the QZE have scarcely been investigated thus far. We have addressed these issues by showing that (i) the QZE is principally unattainable in radiative or radioactive decay, because the required measurement rates would cause the system to disintegrate; (ii) decay acceleration by frequent measurements (the anti-Zeno effect -- AZE) is much more ubiquitous than its inhibition. The AZE is shown to be observable as the enhancement of tunneling rates (e.g., for atoms trapped in ramped-up potentials or in current-swept Josephson junctions), fluorescence rates (e.g., for Rydberg atoms perturbed by noisy optical fields) and photon depolarization rates (in randomly modulated Pockels cells).
The term 'quantum Zeno paradox' or 'quantum Zeno effect' refers to the slowing down of the evolution of a quantum system as it is observed more and more frequently.In 1977, Misra and Sudarshan gave a theoretical demonstration of its existence.There has been disagreement regarding the definition of the effect and whether it is really a paradox, requiring new physics, or a consequence of ordinary quantum mechanics.The experiment of Itano, Heinzen, Bollinger and Wineland, published in 1990, is the one most often called a demonstration of the quantum Zeno effect.Some different interpretations are discussed.
Summary form only given. The quantum Zeno effect (QZE) is the striking possibility of inhibiting the decay of an unstable quantum state by sufficiently frequent measurements. This effect is currently believed to be universal, even though it has only been observed for oscillations between discrete states. Recently we showed that both the QZE and the inverse (anti-) Zeno effect (AZE) can be observed on spontaneous decay in cavities. We develop a general theory of evolution of quantum systems in the presence of frequent measurements. We consider both the ideal case of instantaneous projections of the wave function to the initial state and some possible measurement schemes. The considerations imply the impossibility of the continuous-observation limit necessary to stop quantum evolution (the quantum Zeno paradox). Indeed, this limit leads to an unbounded increase of the energy fluctuations of the system, which would cause the system to disintegrate. The present theory describes different measurement effects, including the QZE and AZE, and allows us to obtain the general criteria of their validity. In particular, we show that the AZE, rather than the QZE, is achievable for spontaneous decay of atoms in free space.
The quantum Zeno effect is a striking feature of quantum mechanics with foundational implications and practical applications in quantum control, error suppression, and error correction. In recent years, the effect has branched off into a variety of different interpretations, making it easy to miss its underlying unifying features. In particular, the quantum Zeno effect has been studied in the context of both selective and nonselective measurements; for both pulsed and continuous interactions; for suppression and enhancement of decay (Zeno / anti-Zeno effects); and even in the absence of measurement entirely. This tutorial presents a unified picture of these effects by examining how they all arise in the pedagogical example of a driven qubit subjected to measurements or dissipation. Zeno and anti-Zeno effects appear as regimes of a unified effect that appears when a measurement-like process competes with non-commuting evolution. The current landscape of Zeno and anti-Zeno effects is examined through this unifying lens, with a focus on experimental applications and implementations. Thus, this tutorial is ideal for new researchers interested in learning about cutting-edge tools in quantum control and measurement, while remaining highly relevant to quantum computing specialists aiming to understand the quantum Zeno effect's applications in adjacent subfields or apply it in a novel way in their own research. The quantum Zeno effect is found to be both ubiquitous and essential for the future of near-term quantum computing.