Generalised quantum Stein lemma robust for broader quantum state sources
Generalised quantum Stein's lemma more robust than ever
Information Theory
Summary
Scientists study how to tell quantum states apart, which is important for quantum technologies. Past work only rigorously handled states that looked like repeated copies of the same state or closely related ones. This paper proves that the main tool for this task works even for much more general types of quantum states, using a new mathematical distance concept. This widens the situations where quantum hypothesis testing can be trusted and understood.
What this means in practice
- •For quantum algorithm developers: Design hypothesis tests that reliably distinguish quantum states even when the input states vary in complex ways beyond simple repetition.
- •For quantum communication engineers: Evaluate error rates and security limits in quantum communication protocols with varying or fluctuating quantum sources.
A theory result. No direct application yet.
Authors
Filippo Girardi, Kuan-Yi Lee, Masahito Hayashi, Ludovico Lami
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.