Bhattacharyya statistical divergence of quantum observables

TL;DR

This paper introduces the use of Bhattacharyya statistical divergence to quantify the similarity between probability distributions of quantum observables, with explicit formulas for spin-1/2 systems and potential physical measurement applications.

Contribution

It applies Bhattacharyya divergence to quantum observables, providing explicit formulas for spin-1/2 systems and exploring its physical measurement relevance.

Findings

Derived explicit Bhattacharyya divergence for spin-1/2 observables.

Demonstrated the divergence's application to non-commuting quantum observables.

Suggested potential use in quantum measurement analysis.

Abstract

In this article we exploit the Bhattacharyya statistical divergence to determine the similarity of probability distributions of quantum observables. After brief review of useful characteristics of the Bhattacharyya divergence we apply it to determine the similarity of probability distributions of two non-commuting observables. An explicit expression for the Bhattacharyya statistical divergence is found for the case of two observables which are the x- and z-components of the angular momentum of a spin-1/2 system. Finally, a note is given of application of the considered statistical divergence to the specific physical measurement.