Generalised quantum Stein's lemma more robust than ever

2026-09-15

AI Summary

本文解决了量子假设检验中更广泛来源的问题，通过使用归一化量子Wasserstein距离方法，扩展了广义量子Stein引理的应用范围。

Abstract

The generalised quantum Stein's lemma is a key result in quantum hypothesis testing, and connects this fundamental primitive of quantum information processing with quantum resource manipulation, a task that is central for technological applications. Prior works have proved this statement in the idealised setting of independent and identically distributed (i.i.d.) sequences of quantum states, and recent extensions consider also sources that are 'close' to i.i.d., according to the strict notion put forth by Mazzola, Sutter, and Renner. For several applications, however, one would need to consider yet more general sources. We establish a version of the generalised quantum Stein's lemma that is conceptually much simpler and general, as it applies to any source that is asymptotically close to an i.i.d. state with respect to the normalised quantum Wasserstein distance of order 1. As an immediate consequence, we solve the Stein exponent of a scenario where the null hypothesis is arbitrarily varying, expressing it in terms of i.i.d. Stein exponents corresponding to arbitrary states in the convex hull of the null hypothesis base set.

Problem

• generalised quantum Stein's lemma
• quantum hypothesis testing
• asymptotically close
• normalised quantum Wasserstein distance

Innovation

• generalised quantum Stein's lemma
• quantum Wasserstein distance
• asymptotically close to i.i.d.
• Stein exponent