Exact exponents for smoothing the max-relative entropy and quantum information decoupling in von Neumann algebras

@misc{lin2026exact,
  title = {{Exact exponents for smoothing the max-relative entropy and quantum information decoupling in von Neumann algebras}},
  author = {Zhiwen Lin and Hongsen Qiu and Xinyu Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.07997},
  eprint = {2607.07997},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.07997},
}

TY  - UNPB
TI  - Exact exponents for smoothing the max-relative entropy and quantum information decoupling in von Neumann algebras
AU  - Zhiwen Lin
AU  - Hongsen Qiu
AU  - Xinyu Zhang
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2607.07997
UR  - https://arxiv.org/abs/2607.07997
AB  - We establish the exact exponent for smoothing the max-relative entropy on arbitrary von Neumann algebras. The proof first develops the required large-deviation and smoothing estimates in the semifinite setting and then passes to general von Neumann algebras through Haagerup-Junge-Xu reduction. We next study catalytic quantum information decoupling when the reference system is described by an arbitrary von Neumann algebra. A key ingredient is an operator layer-cake formula valid on arbitrary von Neumann algebras. This formula leads to a convex-split estimate for normal states with a general von Neumann algebraic reference system. Combining this estimate with the smoothing exponent result, we obtain lower and upper bounds on the catalytic-decoupling reliability function. These bounds coincide below the corresponding critical rate, yielding the exact decoupling reliability function in that regime.
ER  -