A Matrix Version of Law of Large Numbers and Its Relation to Quantum Hypothesis Testing

摘要

We show an asymptotic characterization of the quantum relative entropy, whose classical counterpart is a direct consequence of the law of large numbers, and discuss its relation to the quantum version of Stein's lemma for a hypothesis testing problem on quantum states. This characterization is expected to play an essential role to understand several asymptotics in quantum information theory in a unified manner.