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arXiv:1310.2504 · Annals of Physics

Notes on nonlocal projective measurements in relativistic systems

Shih-Yuin Lin

Published Oct 13, 2014• 10 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2014.08.018

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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.
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.