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Instantaneous Measurement of Nonlocal Variables

Richard A. Low

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

We ask the question: is it possible to measure nonlocal properties of a state instantaneously? Relativistic causality restricts how this can be done, but we show here, for the bipartite two dimensional case, that every nonlocal variable of the system can be measured instantaneously. A necessary condition for a general nonlocal measurement on a bipartite system is presented.

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Experimental proposal for performing nonlocal measurement of a product observable

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Due to the restrictions on quantum measurement imposed by relativistic causality, it is not easy to perform a nonlocal measurement on spacelike separated systems instantaneously. Here we design an experiment in an optical system to perform the nonlocal measurement of a product observable on a two-qubit system, where a maximally-entangled two-qubit state, acting as an ancillary meter, and three identical Kerr media are used to couple the system under consideration and the target meter. It is shown that the nonlocal measurement of the product observable, σzA⊗σzB, which has two degenerate eigenvalues, could be implemented in a deterministic way without violating relativistic causality.

Optics Express•Nov 15, 2016•8 citations
We ask the question: is it possible to measure nonlocal properties of a state instantaneously? Relativistic causality restricts how this can be done, but we show here, for the bipartite two dimensional case, that every nonlocal variable of the system can be measured instantaneously. A necessary condition for a general nonlocal measurement on a bipartite system is presented.
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.
We report results of an investigation of relativistic causality constraints on the measurability of nonlocal variables. We show that measurability of certain nondegenerate variables with entangled eigenstates contradicts the principle of causality, but that there are other, certainly nonlocal, variables which can be measured without breaking causality. We show that any causal measurement of nonlocal variables must erase certain local information. For example, for a system of two spin-1/2 particles, even if we take the weakest possible definition of verification measurement, verification of an entangled state must erase all local information.
Due to the restrictions on quantum measurement imposed by relativistic causality, it is not easy to perform a nonlocal measurement on spacelike separated systems instantaneously. Here we design an experiment in an optical system to perform the nonlocal measurement of a product observable on a two-qubit system, where a maximally-entangled two-qubit state, acting as an ancillary meter, and three identical Kerr media are used to couple the system under consideration and the target meter. It is shown that the nonlocal measurement of the product observable, σzA⊗σzB, which has two degenerate eigenvalues, could be implemented in a deterministic way without violating relativistic causality.