Minimum-error state discrimination and Fano's inequality

TL;DR

This paper explores the relationship between the minimum-error quantum state discrimination and Fano's inequality, analyzing how close the inequality's bounds are to optimal error probabilities across various scenarios.

Contribution

It provides a comparative analysis of minimum-error discrimination and Fano's inequality bounds in quantum state discrimination, including cases with analytical solutions.

Findings

Fano's inequality bounds can be close to minimum-error probabilities in certain scenarios.

Analytic treatments reveal the gap between bounds and optimal error probabilities.

The work enhances understanding of error bounds in quantum state discrimination.

Abstract

The discrimination between non-orthogonal quantum states plays a pivotal role in quantum information processing and quantum technology. Strategies that minimize the error probability are of particular importance, but they are only known for special classes of problems. Certain forms of Fano's inequality yield a bound on the error probability, but it is not known how close this bound is to the minimum-error probability achieved by means of optimal measurements. In this work we discuss how the minimum-error probability compares to the error bound obtained through the Fano's inequality for several scenarios, some of which are amenable to analytic treatments.