Bhattacharyya statistical divergence of quantum observables

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.