当经典关联认证纠缠恢复时
When Classical Correlations Certify Entanglement Recovery
- The University of Tokyo（东京大学）
- Nagoya University（名古屋大学）
- Institute of Science Tokyo（东京科学大学）
- Kyoto University（京都大学）
- RIKEN Center for Quantum Computing (RQC)（理化学研究所量子计算中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过引入比互补性更宽松的不可约性条件，建立了纠缠与态可区分性之间的定量联系，并应用于纠缠蒸馏、量子纠错及测量权衡，提出了统一框架。
AI中文摘要：
纠缠和态的可区分性长期以来一直是量子基础中的核心主题。虽然每一个都各自发展成为一个丰富的研究领域，但它们可以通过互补基中的测量联系起来。这种联系提供了对量子与经典关联的洞察，并支撑了许多信息处理任务，尤其是量子纠错（QEC）。然而，纠缠与可区分性之间的联系是否能在不假设互补性的情况下扩展到一般测量，这一问题在很大程度上仍然悬而未决。我们肯定地回答了这个问题：关键在于由测量引起的不可约性，这是一个比互补性宽松得多的条件。具体来说，对于满足不可约性条件的POVM，我们建立了将一侧局域变换为最大纠缠态的保真度损失与态判别失败概率之间的定量关系。然后我们刻画了何时两种误差可以同时消失。我们的结果直接应用于纠缠蒸馏和QEC。它们的误差可以通过从实验上可访问的局域测量中估计经典输入-输出关联来认证，而无需互补性。这些结果也扩展到量子测量理论。我们推导了新的权衡关系，这些关系连接了两种历史上不同的方法：信息增益-不可逆性和可观测噪声-扰动。因此，我们通过不可约性建立的纠缠与可区分性之间的联系，为纠缠蒸馏、QEC和测量权衡提供了一个共同框架。
英文摘要：
Entanglement and state distinguishability have long been central topics in quantum foundations. While each has developed into a rich subject in its own right, they can be connected through measurements in complementary bases. This connection provides insights into quantum and classical correlations and underlies many information-processing tasks, most notably quantum error correction (QEC). However, it has remained largely open whether the connection between entanglement and distinguishability extends to general measurements without assuming complementarity. We answer this question in the affirmative: the key is irreducibility induced by measurements, a much more relaxed condition than complementarity. Specifically, for POVMs satisfying an irreducibility condition, we establish a quantitative relation between the infidelity of one-sided local transformation into a maximally entangled state and the failure probability in state discrimination. We then characterize when both errors can vanish simultaneously. Our results have direct applications to entanglement distillation and QEC. Their errors can be certified by estimating classical input-output correlations from experimentally accessible local measurements, without requiring complementarity. The results also extend to quantum measurement theory. We derive novel trade-off relations that bridge two historically distinct approaches: information gain--irreversibility and observable noise--disturbance. Our connection between entanglement and distinguishability via irreducibility thus offers a common framework for entanglement distillation, QEC, and measurement trade-offs.
