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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Measurement process in relativistic quantum theory

Yakir Aharonov, David Z. Albert, Lev Vaidman A

Published Sep 15, 1986• 73 citations
Publisher

Abstract

An instantaneous nondemolition measurement technique for composite quantum-mechanical systems (those which consist of several separate subsystems) is described, and that technique is applied to the design of verification experiments for some nonlocal variables and states. Relativistic restrictions on the measurability of nonlocal properties are derived, and other, less familiar, varieties of measurement are discussed.

DOI
10.1103/physrevd.34.1805

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An instantaneous nondemolition measurement technique for composite quantum-mechanical systems (those which consist of several separate subsystems) is described, and that technique is applied to the design of verification experiments for some nonlocal variables and states. Relativistic restrictions on the measurability of nonlocal properties are derived, and other, less familiar, varieties of measurement are discussed.
We study the instantaneity of the state-reduction process in relativistic quantum mechanics. The conclusion of various authors that this instantaneity will restrict the set of relativistic observables to purely local ones (i.e., that the measurement of any nonlocal property of a system at a well-defined time would give rise to violations of relativistic causality) is found to be erroneous, and experiments (of a kind not encountered before in measurement theory) are described whereby certain nonlocal properties of some simple physical systems can be measured at a well-defined time without violating causality. The attempts of certain authors to reconcile the reduction process with the covariance of the relativistic quantum state are considered and found wanting, and it is argued that the covariance of relativistic quantum theories resides exclusively in the experimental probabilities, and not in the underlying quantum states. The problem of nonlocal measurement is considered in general: distinctions (which are not to be met with in the nonrelativistic case) arise in relativistic quantum mechanics between what can be measured for fermions and what can be measured for bosons, between what can be measured for individual systems and what can be measured for ensembles, and between what kinds of states can be verified by measurement and what kinds of states can be prepared by measurement; and these pose difficult questions about the nature of measurement itself.
This article reviews six historically important papers in the development of the theory of measurement for nonlocal variables in quantum mechanics, with special emphasis the non violation of relativistic causality. Spanning more than seventy years, we chart the major developments in the field from the declaration, by Landau and Peierls in 1931, that measurement of nonlocal variables was impossible in the relativistic regime to the demonstration, by Vaidman in 2003, that all such variables \emph{can} be measured instantaneously without violation of causality through an appropriate act of "measurement", albeit not of a standard projective (Von Neumann) type.
Consequences of relativistic causality for measurements of nonlocal characteristics of composite quantum systems are investigated. It is proved that verification measurements of entangled states necessarily erase local information. A complete analysis of measurability of nondegenerate spin operators of a system of two spin-1/2 particles is presented. It is shown that measurability of certain projection operators which play an important role in axiomatic quantum theory contradicts the causality principle.