Single-outcome information gain of qubit measurements on different state ensembles

Abstract

We calculate the single-outcome information gain of quantum measurements on a completely unknown qubit state randomly chosen from different state ensembles. It is shown that the information gain decreases when the ensemble size increases. We obtain analytic single-outcome information gain formulas for continuous equatorial and spherical state ensembles, which show that the states in the former ensemble are relatively easier to identify. The squared fidelity between post-measurement state and pre-measurement state is also calculated, and the qualitative tradeoff relations between information gain and fidelity are illustrated by our results.