Another quantum version of Sanov theorem

We study how to extend Sanov theorem to the quantum setting. Although a quantum version of the Sanov theorem was proposed in Bjelakovic et al (Commun. Math. Phys., 260, p.659 (2005)), the classical case of their statement is not the same as Sanov theorem because Sanov theorem discusses the behavior of the empirical distribution when the empirical distribution is different from the true distribution, but they studied a problem related to quantum hypothesis testing, whose classical version can be shown by classical Sanov theorem. We propose another quantum version of Sanov theorem by considering the quantum analog of the empirical distribution.