包含极小局部不可区分性：一种弱形式的非定域性
Inclusion-Minimal local indistinguishability: a weak form of nonlocality
浏览论文内容
中文总结 AI 辅助
本文提出包含极小局域不可区分集合概念，证明有限局域不可区分集合含此类子集，发现双副本可区分该集合，还构造了特定维度空间中的此类乘积态集合，为量子非定域性结构提供补充视角。
中文摘要 AI 辅助
量子态的局域区分是分布式量子信息处理中的基础任务，是量子通信、数据隐藏、秘密共享等应用的基础。本文研究一种弱形式的局域不可区分性，探究当候选集合被缩减或提供未知态的额外副本时，这种不可区分性会以多快的速度消失。我们引入包含极小局域不可区分集合的概念，即每个真子集都可通过局域操作和经典通信（LOCC）实现完美区分的局域不可区分集合，证明每个有限局域不可区分集合都包含此类子集。我们进一步发现，当拥有两个相同副本时，任何包含极小局域不可区分集合都可通过LOCC实现完美区分，而单个副本则不足以做到这一点。最终，我们在$(\bolde^d)^{\boxtimes n}$中为每个奇数$d=2k+1$和$n\bo2$构造了明确的包含极小局域不可区分乘积态集合。这些结果表明，局域不可区分性在单副本层面可具有非平凡性，但在移除候选态或适度增加副本资源时会变得脆弱，为量子非定域性的结构提供了补充视角。
英文摘要
Local discrimination of quantum states is a fundamental task in distributed quantum information processing and underlies applications such as quantum communication, data hiding, and secret sharing. Here we investigate a weak form of local indistinguishability by asking how easily it can disappear when the candidate set is reduced or an additional copy of the unknown state is supplied. We introduce inclusion-minimal locally indistinguishable sets, namely, locally indistinguishable sets for which every proper subset is perfectly distinguishable by local operations and classical communication (LOCC), and show that every finite locally indistinguishable set contains such a subset. We further find that any inclusion-minimal locally indistinguishable sets becomes perfectly distinguishable by LOCC when two identical copies are available, although a single copy is insufficient. Fininally, We construct explicit inclusion-minimal locally indistinguishable product-state sets in $(\mathbb C^d)^{\otimes n}$ for every odd $d=2k+1$ and $n\ge2$. These results show that local indistinguishability can be nontrivial at the single-copy level yet fragile under either the removal of candidate states or a modest increase in copy resources, providing a complementary perspective on the structure of quantum nonlocality.
