发表机构
University of Copenhagen; University of Waterloo; Cornell University（哥本哈根大学; 滑铁卢大学; 康奈尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种 Log-Euclidean Rényi 条件互信息，满足单调性、可加性等理想性质，并基于恢复态给出 QCMI 的上下界及新颖的 Rényi 链式法则。
AI 中文摘要
量子条件互信息（QCMI）是条件独立性的基本度量，在量子信息理论和多体物理中具有核心应用。尽管其重要性不言而喻，但找到一个满足所有理想结构性质的完全量子 Rényi 推广仍然是一个悬而未决的问题。在这项工作中，我们引入了一种具有这些理想性质的量子 Rényi 条件互信息：它在局部量子信道下单调，在张量积下可加，在 Rényi 参数下单调，并在极限 $\alpha \to 1$ 时收敛到 QCMI。我们建立了该量相对于 Petz 恢复态的相对熵的界限，表明它提供了近似条件独立性的独特度量。作为推论，我们推导了基于恢复的 QCMI 上下界，这些界以 Kullback-Leibler 散度的量子推广形式给出，在某些情况下改进了已知的最佳结果。最后，我们建立了相对于马尔可夫态和可分离态集合的相对熵的界限，并推导了 Rényi 链式法则，这些法则即使在经典情形下也似乎是新颖的。
英文摘要
Quantum conditional mutual information (QCMI) is a fundamental measure of conditional independence, with central applications throughout quantum information theory and many-body physics. Despite its importance, finding a fully quantum Rényi generalization that satisfies all desirable structural properties has remained an open question. In this work, we introduce a quantum Rényi conditional mutual information possessing these desirable properties: it is monotone under local quantum channels, additive under tensor products, monotone in the Rényi parameter, and converges to the QCMI in the limit $α\to 1$. We establish bounds on this quantity in terms of relative entropies to the Petz-recovered state, showing that it provides a distinct measure of approximate conditional independence. As a consequence, we derive recovery-based upper and lower bounds on the QCMI in terms of quantum generalizations of the Kullback-Leibler divergence, improving upon the best known results in certain regimes. Finally, we establish bounds in terms of relative entropies to the sets of Markov and separable states and derive Rényi chain rules, which appear to be novel even in the classical setting.
