Sharp Data-Processing Region for Quantum Conditional R\'enyi Entropies

Abstract:We study the three-parameter family of quantum conditional Rényi entropies $H_{\alpha,z}^\lambda$ 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 $z = \alpha$. 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.

arXiv:2609.31350 [quant-ph]

(or arXiv:2609.31350v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.31350 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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