A Generalized quantum Stein lemma on von Neumann algebras

We prove a generalized quantum Stein lemma for i.i.d. normal states against convex, tensor-stable families on arbitrary von Neumann algebras. Assuming the existence of an alternative state with finite relative entropy from the null state, we show that, at every type-I error tolerance $\varepsilon\in (0,1)$, the worst case type-II error exponent is achieved with the regularized relative entropy with a strong converse. The proof combines the integral representation of relative entropy by hockey-stick divergences, a modular testing bound, and convex minimax argument.

Source: arXiv:2610.02134v1 - http://arxiv.org/abs/2610.02134v1 PDF: https://arxiv.org/pdf/2610.02134v1 Original Link: http://arxiv.org/abs/2610.02134v1