Analytical bounds for non-asymptotic asymmetric state discrimination

TL;DR

This paper derives explicit, non-asymptotic bounds for asymmetric quantum state discrimination errors, providing more precise finite-copy error estimates using trace norm, fidelity, and Chernoff bounds, with tightness in certain cases.

Contribution

It introduces explicit bounds on achievable errors in non-asymptotic asymmetric quantum state discrimination, including tight bounds for pure states and finite-copy scenarios.

Findings

Upper bounds are asymptotically tight.

Lower bounds are exact for pure states.

Bounds provide finite-copy error estimates, not just exponents.

Abstract

Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding the set of achievable errors, using the trace norm, the fidelity, and the quantum Chernoff bound. The upper bound is asymptotically tight and the lower bound is exact for pure states. Unlike asymptotic bounds, our bounds give error values instead of exponents, so can give more precise results when applied to finite-copy state discrimination problems.