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NeuroQuantology

Quantum Zeno Effect in Sleep Disorders and Treatment by the Anti-Zeno Effect

Rajat Kumar Pradhan

Published Oct 16, 2015• 0 citations
Publisher

Abstract

It is proposed on the basis of a recent quantum mechanical approach to the states of consciousness that for those sleep disorders of psychological origin which can be considered to be a Quantum Zeno Effect-type phenomenon of persistence in the waking state due to the inhibition of the transition to the Deep Sleep state, the treatment may very well lie in the application of the principle of accelerating the decay by the introduction of a third state which facilitates the transition as realized in the Quantum Anti-Zeno effect. Steps of practical therapeutic implementation of the program are delineated as an appendix.

DOI
10.14704/nq.2016.14.1.864

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It is proposed on the basis of a recent quantum mechanical approach to the states of consciousness that for those sleep disorders of psychological origin which can be considered to be a Quantum Zeno Effect-type phenomenon of persistence in the waking state due to the inhibition of the transition to the Deep Sleep state, the treatment may very well lie in the application of the principle of accelerating the decay by the introduction of a third state which facilitates the transition as realized in the Quantum Anti-Zeno effect. Steps of practical therapeutic implementation of the program are delineated as an appendix.
It is proposed that for those sleep disorders of psychological origin which can be considered to be a Quantum Zeno Effect-type phenomenon of persistence in the waking state due to the inhibition of the transition to the Deep Sleep state, the treatment may very well lie in the application of the principle of accelerating the decay by the introduction of a third state which facilitates the transition as realized in the Quantum Anti-Zeno effect. Steps of practical therapeutic implementation of the program are delineated.
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.
In 1977, Mishra and Sudarshan [J. Math. Phys. 18, 756 (1977)] showed that an unstable particle would never be found decayed while it was continuously observed. They called this effect the quantum Zeno effect (or paradox). Later it was realized that the frequent measurements could also accelerate the decay (quantum anti-Zeno effect). In this paper, we investigate the quantum Zeno effect using the definite model of the measurement. We take into account the finite duration and the finite accuracy of the measurement. A general equation for the jump probability during the measurement is derived. We find that the measurements can cause inhibition (quantum Zeno effect) or acceleration (quantum anti-Zeno effect) of the evolution, depending on the strength of the interaction with the measuring device and on the properties of the system. However, the evolution cannot be fully stopped.
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.