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arXiv:1111.5227

Quantum Anti-Zeno Treatment of Zeno-type Sleep Disorders

Rajat Kumar Pradhan

Published Nov 20, 2011• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1111.5227

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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.
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.
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.
A simple model of indirect pre-measurements on an unstable quantum state is presented in this paper. The model is completely solvable and the solutions are used to compare the time evolution of the unstable state with and without the influence of the pre-measurement. We find that by choosing the details of the process of pre-measurement appropriately, it is possible to observe both suppression and enhancement of the rate of decay of the unstable state. When the pre-measurements are assumed to lead on to actual measurements, we see that the quantum Zeno effect, and in some instances the 'anti-Zeno' effect, can be produced by repeating the measurement many times in succession. The Zeno effect can appear in our model either as a real consequence of repeated measurements or sometimes merely as an artefact of the manner in which the observations on the system are performed. The anti-Zeno effect appears almost exclusively as an artefact of the details of the measurement. Numerical investigations are included to delineate the regimes in which the quantum Zeno effect and possibly the anti-Zeno effect can occur.