最大纠缠态判别中单向与双向LOCC之间的多项式分离
Polynomial Separation between One-Way and Two-Way LOCC in Discrimination of Maximally Entangled States
- Chungbuk National University（忠北国立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究证明在最大纠缠态判别中，通过单次反馈的双向LOCC可将可区分候选态数量从常数提升至多项式级，实现单向与双向LOCC的分离，并给出九份拷贝的充分性结论。
AI中文摘要：
在任意局部维度 $d\ge4$ 中，单向局域操作与经典通信（LOCC）可能无法区分四个正交的最大纠缠态。我们证明，在 $\mathbb C^d\otimes\mathbb C^d$ 中，当 $d\ge Ck^4[\log(2k)]^\nu$ 时（其中 $C,\nu>0$ 为普适常数），任意 $k$ 个两两正交的最大纠缠态集合都能通过 $A\to B\to A$ 协议被完美区分。因此，单次反馈消息将总能区分的候选态数量从常数提升至 $\Omega\\!\left(d^{1/4}/(\log d)^{\nu/4}\right)$，确立了单向与双向LOCC之间的多项式分离。在我们的协议中，Alice在减少Bob条件子空间之间重叠的同时保持精确正交性。Bob将候选态缩减为单例或正交对，并细化其测量结果，使得Alice能够完成判别。作为推论，在所有足够大的局部维度中，九份拷贝足以对任意正交最大纠缠态集合实现完美的双向LOCC判别。
英文摘要：
One-way local operations and classical communication (LOCC) can fail to distinguish four orthogonal maximally entangled states in every local dimension $d\ge4$. We show that every set of $k$ pairwise orthogonal maximally entangled states in $\mathbb C^d\otimes\mathbb C^d$ is perfectly distinguishable by an $A\to B\to A$ protocol whenever $d\ge Ck^4[\log(2k)]^ν$, for universal constants $C,ν>0$. A single feedback message therefore raises the number of candidates that can always be distinguished from a constant to $Ω\!\left(d^{1/4}/(\log d)^{ν/4}\right)$, establishing a polynomial separation between one-way and two-way LOCC. In our protocol, Alice preserves exact orthogonality while reducing overlaps between Bob's conditional subspaces. Bob reduces the candidates to a singleton or an orthogonal pair and refines his outcome so that Alice can complete the discrimination. As a corollary, nine copies suffice for perfect two-way LOCC discrimination of any orthogonal maximally entangled set in all sufficiently large local dimensions.
