量子条件Rényi熵的尖锐数据处理区域

中文摘要 AI 辅助

我们研究了《数学物理通讯》407, 180 (2026) 中引入的三参数量子条件Rényi熵族 $H_{\alpha,z}^\lambda$。我们证明了先前建立的数据处理区域是尖锐的。然后，我们通过经典粗粒化原理刻画了三明治夹心族：在完整数据处理区域内，经典条件寄存器在确定性粗粒化下的普适单调性成立当且仅当 $z = \alpha$。最后，我们通过证明有限维三方纯态的任何普适对偶关系必须满足已知参数关系，建立了熵对偶的刚性。因此，数据处理区域、三明治夹心子族和对偶变换各自通过其相应的普适性质被唯一刻画。

英文摘要

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.

发表机构

• National University of Singapore（新加坡国立大学）
• Xi’an Jiaotong-Liverpool University（西交利物浦大学）

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