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Journal of Physics A Mathematical and General

A critical re-examination of the quantum Zeno paradox

Dipankar Home, M. A. B. Whitaker

Published Feb 7, 1992• 37 citations
Publisher

Abstract

The quantum Zeno paradox is defined as a negative-result experiment involving a macroscopic apparatus, and distinguished from other quantum Zeno processes. It is demonstrated that collapse of state-vector is not a requirement for the paradox, which is independent of interpretation of quantum theory. Gedanken experiments are outlined which illustrate the key features of the paradox, and its implications for the realist interpretation are discussed.

DOI
10.1088/0305-4470/25/3/022

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The quantum Zeno paradox is defined as a negative-result experiment involving a macroscopic apparatus, and distinguished from other quantum Zeno processes. It is demonstrated that collapse of state-vector is not a requirement for the paradox, which is independent of interpretation of quantum theory. Gedanken experiments are outlined which illustrate the key features of the paradox, and its implications for the realist interpretation are discussed.
The quantum Zeno paradox is examined within the many-worlds and relative states interpretations of quantum mechanics. In the many-worlds interpretation the effect is predicted to persist. The possibility of recombining worlds is not expected to be relevant. In the simplest form of relative states interpretation the effect may be avoided but this form of interpretation experiences difficulties in coping with conventional problems of quantum theory. The more complex version of the relative states interpretation, which takes account of the correlations of system with apparatus, predicts the occurrence of the paradox.
As of October 2006, there were approximately 535 citations to the seminal 1977 paper of Misra and Sudarshan that pointed out the quantum Zeno paradox (more often called the quantum Zeno effect). In simple terms, the quantum Zeno effect refers to a slowing down of the evolution of a quantum state in the limit that the state is observed continuously. There has been much disagreement as to how the quantum Zeno effect should be defined and as to whether it is really a paradox, requiring new physics, or merely a consequence of "ordinary" quantum mechanics. The experiment of Itano, Heinzen, Bollinger, and Wineland, published in 1990, has been cited around 347 times and seems to be the one most often called a demonstration of the quantum Zeno effect. Given that there is disagreement as to what the quantum Zeno effect is , there naturally is disagreement as to whether that experiment demonstrated the quantum Zeno effect. Some differing perspectives regarding the quantum Zeno effect and what would constitute an experimental demonstration are discussed.
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.
The authors clarify some of the controversial aspects involved in the treatment of the quantum Zeno paradox. An argument for the paradox is given on the basis of the uncertainty principle, and the conditions for the paradox are analysed. Fleming's rule is proved in a simple way. Connection with the standard time-dependent perturbation theory is discussed. They compare the Zeno paradox with the other well known paradoxes of quantum mechanics and point out that the quantum Zeno paradox is immune to the use of the ensemble interpretation which has some success in tackling the other paradoxes. Remarks are made concerning the broader significance of the quantum Zeno paradox.
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.
Technological advances have made it possible to perform experiments, once considered to be purely gedanken, which test the counterintuitive and bizarre consequences of quantum theory. This book provides simple accounts of these experiments and an understanding of what they aim to prove and why this is important. After introducing the main theoretical concepts and problems with the foundations of quantum mechanics, early chapters discuss experiments in the areas of wave-particle duality, cavity quantum electrodynamics and quantum non-demolition measurement. The text then examines investigation of certain predictions including the Aharanov-Bohm effect, before tackling the problem of macroscopic quantum coherence. Later chapters consider methods of testing the quantum Zeno paradox, collapse, macroscopic quantum jumps, tunnelling times and Einstein-Bell non-locality. Introductions to the theory behind types of measuring devices such as micromasers and those based on the concept of quantum non-demolition are also given. Detailed references are included.