Direct tests of measurement uncertainty relations: what it takes

Physical Review Letters
Paul Busch, Neil Stevens

Abstract

The uncertainty principle being a cornerstone of quantum mechanics, it is surprising that, in nearly 90 years, there have been no direct tests of measurement uncertainty relations. This lacuna was due to the absence of two essential ingredients: appropriate measures of measurement error (and disturbance) and precise formulations of such relations that are universally valid and directly testable. We formulate two distinct forms of direct tests, based on different measures of error. We present a prototype protocol for a direct test of measurement uncertainty relations in terms of value deviation errors (hitherto considered nonfeasible), highlighting the lack of universality of these relations. This shows that the formulation of universal, directly testable measurement uncertainty relations for state-dependent error measures remains an important open problem. Recent experiments that were claimed to constitute invalidations of Heisenberg's error-disturbance relation, are shown to conform with the spirit of Heisenberg's principle if interpreted as direct tests of measurement uncertainty relations for error measures that quantify distances between observables.

References

Sep 26, 2012·Physical Review Letters·Lee A RozemaAephraim M Steinberg
Apr 9, 2013·Proceedings of the National Academy of Sciences of the United States of America·Cyril Branciard
Nov 5, 2013·Physical Review Letters·Paul BuschReinhard F Werner
Feb 4, 2014·Physical Review Letters·Martin RingbauerAndrew G White
Feb 4, 2014·Physical Review Letters·Fumihiro KanedaKeiichi Edamatsu

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Citations

Jun 2, 2016·Scientific Reports·Yu-Xiang ZhangZeng-Bing Chen
Apr 2, 2019·Physical Review Letters·Ya-Li MaoJian-Wei Pan

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