For the optimal success probability under minimum-error discrimination between $r\ge 2$ 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.

• Received 13 May 2021
• Accepted 11 January 2022

DOI:https://doi.org/10.1103/PhysRevA.105.032410