General lower and upper bounds under minimum-error quantum state discrimination

Physical Review A: Atomic, Molecular, and Optical physics. 2022. Vol. 105. Article 032410.

Elena R. Loubenets

For the optimal success probability under minimum-error discrimination between $r\geq2$ arbitrary quantum states  prepared  with  any  a  priori  probabilities,  we  find  new  general  analytical  lower  and  upper  bounds  and specify the relations between these new general bounds and the known general bounds, lower and upper. We also present the example where the values of the new general lower and upper bounds on the optimal success probability are tighter than the values of most of the general analytical bounds known in the literature. The new upper bound on the optimal success probability explicitly generalizes to $r>2$ the form of the Helstrom bound. For $r=2$, each of  our new bounds, lower and upper, reduces to the Helstrom bound.

Keywords: quantum information processing, quantum state discrimination, the Helstrom bound, различение квантовых состояний, оценка Хелстрома, обработка квантовой информации