Violation of Heisenberg's error-disturbance uncertainty relation in neutron spin measurements

TL;DR

This study experimentally verifies Ozawa's universally valid error-disturbance relation in neutron spin measurements, demonstrating violations of Heisenberg's original uncertainty relation and challenging the reciprocal error-disturbance assumption.

Contribution

The paper provides the first experimental confirmation of Ozawa's relation in neutron spin measurements using a tomographic approach, overcoming previous inaccessibility issues.

Findings

Heisenberg's original relation is violated in neutron spin measurements.

Ozawa's relation holds true in the tested scenarios.

The reciprocal error-disturbance assumption is invalid in general.

Abstract

In its original formulation, Heisenberg's uncertainty principle dealt with the relationship between the error of a quantum measurement and the thereby induced disturbance on the measured object. Meanwhile, Heisenberg's heuristic arguments have turned out to be correct only for special cases. A new universally valid relation was derived by Ozawa in 2003. Here, we demonstrate that Ozawa's predictions hold for projective neutron-spin measurements. The experimental inaccessibility of error and disturbance claimed elsewhere has been overcome using a tomographic method. By a systematic variation of experimental parameters in the entire configuration space, the physical behavior of error and disturbance for projective spin-1/2 measurements is illustrated comprehensively. The violation of Heisenberg's original relation, as well as, the validity of Ozawa's relation become manifest. In addition, our results conclude that the widespread assumption of a reciprocal relation between error and disturbance is not valid in general.