Direct tests of measurement uncertainty relations: what it takes

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 {\em universally valid}and {\em 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 {\em 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 {\em 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 {\em distances between observables}.

arXiv comment8 pages including Supplement. This version 2 has been substantially rewritten, including a change of title

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• Optimal joint measurements of complementary observables by a single trapped ion
• Heisenberg's error-disturbance relations: a joint measurement-based experimental test
• Stronger Error Disturbance Relations for Incompatible Quantum Measurements
• Quantum Uncertainty and Error-Disturbance Tradeoff
• Uncertainty-disturbance relations and applications