最小-雷恩斯相对熵对于精确PPT纠缠蒸馏并不紧
The Min-Rains Relative Entropy Is Not Tight for Exact PPT Entanglement Distillation
中文总结 AI 辅助
该研究否定了最小-雷恩斯相对熵是精确PPT纠缠蒸馏紧界的猜想，通过引入新的单字母上界，揭示了PPT操作下精确纠缠操纵的微妙渐近结构。
中文摘要 AI 辅助
精确纠缠蒸馏可将有噪双体态转化为零误差的最大纠缠态。在完全PPT保操作下，可加的最小-雷恩斯相对熵为正则化蒸馏率提供了单字母上界。2016年以来纠缠理论中的一个有趣问题是，该界是否总是紧的。本文否定了这一问题。关键在于最小-雷恩斯松弛所缺失的张量稳定刚性：每个可行的精确蒸馏效应必须在输入态的支撑上作用为恒等映射。我们利用一个通常非厄米、支撑在值域上的见证者，将这一约束转化为新的单字母上界。对于秩3子空间，我们证明，对所有具有该支撑的态，该上界严格小于最小-雷恩斯相对熵。因此，最小-雷恩斯松弛所丢弃的约束在任意张量幂下仍然相关。我们的结果排除了最小-雷恩斯相对熵作为精确PPT可蒸馏纠缠的闭式公式的可能，并揭示了PPT操作下精确纠缠操纵的微妙渐近结构。
英文摘要
Exact entanglement distillation converts a noisy bipartite state into a maximally entangled state with zero error. Under completely PPT-preserving operations, the additive min-Rains relative entropy provides a single-letter upper bound on the regularized distillation rate. An interesting problem in entanglement theory dating back to 2016 has been whether this bound is always tight. Here we resolve this question in the negative. The key is a tensor-stable rigidity absent from the min-Rains relaxation: every feasible exact-distillation effect must act as the identity on the support of the input state. We convert this constraint into a new single-letter upper bound using a generally non-Hermitian, range-supported witness. For a rank-three subspace, we show this upper bound lies strictly below the min-Rains relative entropy for every state with that support. Thus, the constraint discarded by the min-Rains relaxation remains relevant under arbitrary tensor powers. Our result rules out the min-Rains relative entropy as a closed-form formula for exact PPT distillable entanglement and reveals the subtle asymptotic structure of exact entanglement manipulation under PPT operations.
