Upper and Lower Bounds on Optimal Success Probability of Quantum State Discrimination with and without Inconclusive Results

TL;DR

This paper establishes new upper and lower bounds on the success probability of quantum state discrimination, including scenarios with inconclusive results, improving upon previous bounds through theoretical analysis and numerical validation.

Contribution

It introduces tighter bounds on success probability for quantum state discrimination, with conditions for optimality and extensions to inconclusive measurement scenarios.

Findings

Proposed bounds are tighter than previous results.

Derived necessary and sufficient conditions for bounds to be tight.

Validated bounds through numerical experiments.

Abstract

We propose upper and lower bounds on the maximum success probability for discriminating given quantum states. The proposed upper bound is obtained from a suboptimal solution to the dual problem of the corresponding optimal state discrimination problem. We also give a necessary and sufficient condition for the upper bound to achieve the maximum success probability; the proposed lower bound can be obtained from this condition. It is derived that a slightly modified version of the proposed upper bound is tighter than that proposed by Qiu et al. [Phys. Rev. A 81, 042329 (2010)]. Moreover, we propose upper and lower bounds on the maximum success probability with a fixed rate of inconclusive results. The performance of the proposed bounds are evaluated through numerical experiments.