New general lower and upper bounds under minimum-error quantum state discrimination

TL;DR

This paper introduces new analytical bounds for the success probability in minimum-error quantum state discrimination, generalizing and tightening existing bounds, including the Helstrom bound for two states.

Contribution

The paper derives new general lower and upper bounds for success probability in quantum state discrimination, extending the Helstrom bound to multiple states and demonstrating their tightness.

Findings

New bounds are tighter than existing ones in certain cases

Upper bound generalizes Helstrom bound for multiple states

Bounds reduce to Helstrom bound when r=2

Abstract

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 general bounds known in the literature. We also present the example where the new general analytical bounds, lower and upper, on the optimal success probability are tighter than 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.