  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.
