Neutron optical test of completeness of quantum root-mean-square errors

TL;DR

This paper demonstrates experimentally using neutron optics that a recently proposed quantum error measure is both sound and complete for different types of quantum measurements, addressing a longstanding problem in quantum measurement theory.

Contribution

The paper provides the first neutron optical experimental validation of the completeness of Ozawa's new quantum error measure for various measurement types.

Findings

Confirmed the completeness of Ozawa's error measure experimentally

Validated the measure for both projective and generalized measurements

Addressed a key issue in quantum measurement error quantification

Abstract

One of the major problems in quantum physics has been to generalize the classical root-mean-square error to quantum measurements to obtain an error measure satisfying both soundness (to vanish for any accurate measurements) and completeness (to vanish only for accurate measurements). A noise-operator based error measure has been commonly used for this purpose, but it has turned out incomplete. Recently, Ozawa proposed a new definition for a noise-operator based error measure to be both sound and complete. Here, we present a neutron optical demonstration for the completeness of the new error measure for both projective (or sharp) as well as generalized (or unsharp) measurements.