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. 
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