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A Generalized quantum Stein lemma on von Neumann algebras

  • Li Gao
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Abstract

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 ε∈ (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.

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Cite

BibTeXRIS
BibTeX
@misc{gao2026generalized,
  title = {{A Generalized quantum Stein lemma on von Neumann algebras}},
  author = {Li Gao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02134},
  eprint = {2610.02134},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02134},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Generalized quantum Stein lemma on von Neumann algebras
AU  - Li Gao
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.02134
UR  - https://arxiv.org/abs/2610.02134
AB  - 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 ε∈ (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.
ER  -