带关联催化的PPT纠缠：单调量与不可逆性
PPT Entanglement with Correlated Catalysis: Monotones and Irreversibility
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中文总结 AI 辅助
该研究在PPT资源理论中，利用正则化PPT相对熵构造单调量，证明其完全可加且强超加性，发现关联催化无法消除混态纠缠操纵的基本限制，最优蒸馏率仍小于纠缠成本。
中文摘要 AI 辅助
量子催化剂可在不被消耗的情况下实现原本不可能的量子态变换，使其与输出产生关联会大幅提升这种辅助能力。这引发了纠缠理论的一个基本问题：当这类关联催化剂可自由使用时，态操纵仍存在哪些限制？我们在正部分转置（PPT）资源理论中解答了该问题，该理论允许的操作类别远多于局域操作与经典通信（LOCC）。我们确定了正则化相对熵测度成为强超加性的一般条件，并利用这些条件构造了无需知晓催化剂即可约束关联催化PPT变换的单调量。特别地，我们证明正则化PPT相对熵是完全可加且强超加性的，解决了纠缠理论中的一个开放问题。最重要的是，这些约束表明，即使任意关联催化剂也无法恢复渐近可逆性：对于一个明确的态，最优纠缠蒸馏率仍严格小于纠缠成本。因此，大量催化辅助并未消除混态纠缠操纵的一些基本限制。
英文摘要
Quantum catalysts can overcome otherwise impossible quantum state transformations without being consumed, and allowing them to become correlated with the output makes this assistance substantially more powerful. This raises a fundamental question for entanglement theory: which limitations on state manipulation remain when such correlated catalysts are freely available? We answer this question in the positive-partial-transpose (PPT) resource theory, which allows a substantially broader class of operations than local operations and classical communication (LOCC). We identify general conditions under which regularized relative-entropy measures become strongly superadditive, and use them to construct monotones that constrain correlated catalytic PPT transformations without any knowledge of the catalyst. In particular, we prove that the regularized PPT relative entropy is fully additive and strongly superadditive, resolving an open problem in entanglement theory. Most importantly, these constraints show that even arbitrary correlated catalysts cannot restore asymptotic reversibility: for an explicit state, the optimal entanglement distillation rate remains strictly smaller than the entanglement cost. Thus, substantial catalytic assistance does not remove some of the fundamental limitations of mixed-state entanglement manipulation.
