Tight qubit uncertainty relations studied through weak values in neutron interferometry

TL;DR

This paper experimentally investigates Heisenberg's uncertainty relation using weak values in neutron interferometry, confirming a universally valid error-disturbance relation for quantum measurements.

Contribution

It applies a feedback compensation method to experimentally characterize the error-disturbance relation in neutron interferometry, validating theoretical predictions.

Findings

Uncertainty relation is tightly fulfilled for pure states.

Experimental confirmation of Ozawa's error-disturbance relation.

Weak values enable complete characterization of measurement errors.

Abstract

In its original formulation, Heisenberg's uncertainty principle describes a trade-off relation between the error of a quantum measurement and the thereby induced disturbance on the measured object. However, this relation is not valid in general. An alternative universally valid relation was derived by Ozawa in 2003, defining error and disturbance in a general concept, experimentally accessible via a tomographic method. Later, it was shown by Hall that these errors correspond to the statistical deviation between a physical property and its estimate. Recently, it was discovered that these errors can be observed experimentally when weak values are determined through a procedure named "feedback compensation". Here, we apply this procedure for the complete experimental characterization of the error-disturbance relation between a which-way observable in an interferometer and another observable associated with the output of the interferometer, confirming the theoretically predicted relation. As expected for pure states, the uncertainty is tightly fulfilled.