Sharp Data-Processing Region for Quantum Conditional Rényi Entropies
Abstract
We study the three-parameter family of quantum conditional Rényi entropies Hα,zλ introduced in \textit{Commun. Math. Phys.} 407, 180 (2026). We prove that the previously established data-processing region is sharp. We then characterize the club-sandwiched family through a classical coarse-graining principle: within the full data-processing region, universal monotonicity under deterministic coarse-graining of the classical conditioned register holds if and only if z = α. Finally, we establish rigidity of entropic duality by showing that any universal duality relation for finite-dimensional tripartite pure states must satisfy the known parameter relations. Thus, the data-processing region, the club-sandwiched subfamily, and the duality transformation are each uniquely characterized by their respective universal properties.
Related
- Sharp continuity of quantum conditional entropy
- Multi-Indexed Schatten Quasi- and Anti-Norms and Additivity of Conditional Rényi Entropies
- Von Neumann's Two Quantum Entropies
- Improved Quantum Algorithms for Rényi Entropies Estimation
- Bounds on the minimum orbital period of general static spherical black holes: a sharp upper bound and a conditional lower bound
BibTeX
@misc{goodarzi2026sharp,
title = {{Sharp Data-Processing Region for Quantum Conditional Rényi Entropies}},
author = {Milad M. Goodarzi and Yucheng Bao and Marco Tomamichel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31350},
eprint = {2609.31350},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31350},
}
RIS
TY - UNPB
TI - Sharp Data-Processing Region for Quantum Conditional Rényi Entropies
AU - Milad M. Goodarzi
AU - Yucheng Bao
AU - Marco Tomamichel
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31350
UR - https://arxiv.org/abs/2609.31350
AB - We study the three-parameter family of quantum conditional Rényi entropies H_α,z^λ introduced in \textit{Commun. Math. Phys.} 407, 180 (2026). We prove that the previously established data-processing region is sharp. We then characterize the club-sandwiched family through a classical coarse-graining principle: within the full data-processing region, universal monotonicity under deterministic coarse-graining of the classical conditioned register holds if and only if z = α. Finally, we establish rigidity of entropic duality by showing that any universal duality relation for finite-dimensional tripartite pure states must satisfy the known parameter relations. Thus, the data-processing region, the club-sandwiched subfamily, and the duality transformation are each uniquely characterized by their respective universal properties.
ER -