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Journal of Physics A Mathematical and General

Necessary and sufficient conditions for the quantum Zeno and anti-Zeno effect

Harald Atmanspacher A, Werner Ehm, Tilmann Gneiting

Published Sep 9, 2003• 5 citations
Publisher

Abstract

A necessary and sufficient condition for the occurrence of the quantum Zeno effect is given, refining a recent conjecture of Luo, Wang and Zhang. An analogous condition is derived for the quantum anti-Zeno effect. Both results rely on a formal connection between the quantum (anti-)Zeno effect and the weak law of large numbers.
DOI
10.1088/0305-4470/36/38/307

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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.
Universality vs non-universality on the quantum Zeno effect and the anti-Zeno effect is discussed. It is well-known that the Zeno effect is a result of the branch point effect based on the constraint that the energy spectrum is bounded from below. On the other hand, we show that the anti-Zeno effect arises from the interference of multiple complex poles in the lower half energy plane on a larger time scale compared with the Zeno time. Since the production of extra complex poles depends on the characteristics of the interaction Hamiltonian, we emphasize that the anti-Zeno effect is model-dependent and non-universal, while the Zeno effect is a universal phenomenon independent of the form of the interaction.