Direct tests of measurement uncertainty relations: what it takes

TL;DR

This paper addresses the lack of direct experimental tests of quantum measurement uncertainty relations by proposing new protocols and highlighting open problems in formulating universally valid, directly testable relations.

Contribution

It introduces two forms of direct tests based on different error measures and presents a prototype protocol for testing measurement uncertainty relations.

Findings

Recent experiments align with Heisenberg's principle when interpreted as tests of observable distance measures.

The lack of universal, state-independent error measures remains an open challenge.

Proposed protocols enable direct testing of measurement error and disturbance in quantum mechanics.

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}.