多重负性及渐近纠缠的单字母公式
Multinegativity and single-letter formulas for asymptotic entanglement
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中文总结 AI 辅助
本文提出可计算上界的递减层级以逼近渐近相对熵纠缠，并在两个广泛参数族上建立首个非平凡水平的可加性，从而得到单字母公式，同时构造态反驳了纠缠代价层级有限坍缩的猜想。
中文摘要 AI 辅助
纠缠的研究不可避免地导致正则化的概念，其中度量是在态的无穷多个副本上评估的。单字母公式试图通过对态的一个副本进行计算来使这些渐近纠缠量易于处理，但很少可用。我们引入了关于正部分转置（PPT）态的渐近相对熵纠缠的可计算上界的递减层级。每个固定层级水平的正则化等于该渐近量。因此，任何水平上的可加性都产生单字母公式，即使通常的单副本相对熵是不可加的。我们在第一个非平凡水平上为两个广泛的多参数族建立了这种可加性，这两个族都包含所有Werner态。上界构造也扩展到夹心Renyi散度。该层级激发了$k$-多重负性态，这是双负性态和相关$k$-多重负性态的推广，它为渐近相对熵和精确PPT纠缠代价都提供了显式上界。我们构造了在任意大的深度$k$下为$k$-多重负性的态，这些态分离了先前引入的纠缠代价层级的连续水平，反驳了其有限坍缩的猜想。这些结果提供了依赖于态的单字母公式，同时指出了通用有限水平表征的局限性。
英文摘要
The study of entanglement inevitably leads to the concept of regularization, where measures are evaluated on infinitely many copies of a state. Single-letter formulas try to make these asymptotic entanglement quantities accessible through a calculation on one copy of a state, but are rarely available. We introduce a decreasing hierarchy of computable upper bounds on the asymptotic relative entropy of entanglement with respect to positive-partial-transpose (PPT) states. The regularization of every fixed hierarchy level equals this asymptotic quantity. Additivity at any level therefore yields a single-letter formula, even when the usual one-copy relative entropy is nonadditive. We establish such additivity at the first nontrivial level for two broad multiparameter families, both containing all Werner states. The upper-bound construction also extends to sandwiched Renyi divergences. The hierarchy motivates $k$-multinegative states, a generalization of binegative states and the associated $k$-multinegativity, which gives explicit upper bounds on both the asymptotic relative entropy and exact PPT entanglement cost. We construct states which are $k$-multinegative at arbitrarily large depths $k$ that separate consecutive levels of the previously introduced entanglement-cost hierarchy, disproving its conjectured finite collapse. These results provide state-dependent single-letter formulas while identifying a limitation of universal finite-level characterizations.
发表机构
- Heinrich-Heine-Universität Düsseldorf（杜塞尔多夫大学）
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