Optimal distinction between non-orthogonal quantum states

@article{Peres1998OptimalDB,
title={Optimal distinction between non-orthogonal quantum states},
author={A. Peres and Daniel R. Terno},
journal={Journal of Physics A},
year={1998},
volume={31},
pages={7105-7111}
}

Given a finite set of linearly independent quantum states, an observer who examines a single quantum system may sometimes identify its state with certainty. However, unless these quantum states are orthogonal, there is a finite probability of failure. A complete solution is given to the problem of optimal distinction of three states, having arbitrary prior probabilities and arbitrary detection values. A generalization to more than three states is outlined.