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arXiv 2202.09034quant-ph
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具有特殊量子非定域性的最小量子态集合的界限

Bounds on the smallest sets of quantum states with special quantum nonlocality

Mao-Sheng Li, Yan-Ling Wang

备注：
11 pages, some other minor correction
发表信息：
Quantum 7, 1101 (2023)
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AI总结：

本文提出并研究了局部稳定集合（即保正交测量仅为平凡测量的局部不可约集合），构造了多体系统中局部稳定的正交集合，并给出了最小局部稳定集合大小的上下界，从而完整解答了关于任意维度多体系统中强量子非定域性存在性的开放问题。

摘要：

如果多体系统中的正交态集合在子系统的每个二分下都是局部不可约的，则被称为强量子非定域性 [Phys. Rev. Lett. 122, 040403 (2019)]。在本研究中，我们研究局部不可约集合的一个子类：在每个子系统上，唯一可能的保正交测量是平凡测量。我们将具有此性质的集合称为局部稳定集合。我们发现在两量子比特系统中，局部稳定集合与局部不可区分集合是一致的。然后，我们通过依赖于某些态的子空间的维数，给出了局部稳定集合的刻画。此外，我们在一般多体量子系统中构造了两个正交集合，它们在子系统的每个二分下都是局部稳定的。作为推论，我们得到了对于子系统的每个二分下均局部稳定的最小集合大小的下界和上界。我们的结果对近期一篇论文 [Phys. Rev. A 105, 022209 (2022)] 中提出的一个开放问题（即，我们能否证明对于任意的 $d_i \geq 2$ 且 $1\leq i\leq N$，在 $\mathbb{C}^{d_1} \otimes \mathbb{C}^{d_1}\otimes \cdots \otimes \mathbb{C}^{d_N} $ 中存在强量子非定域性？）给出了完整的回答。与以往所有相关的证明相比，我们这里的证明非常简洁。

英文摘要：

An orthogonal set of states in multipartite systems is called to be strong quantum nonlocality if it is locally irreducible under every bipartition of the subsystems \href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.040403}{Phys. Rev. Lett. \textbf{122}, 040403 (2019)}]. In this work, we study a subclass of locally irreducible sets: the only possible orthogonality preserving measurement on each subsystems are trivial measurements. We call the set with this property is locally stable. We find that in the case of two qubits systems locally stable sets are coincide with locally indistinguishable sets. Then we present a characterization of locally stable sets via the dimensions of some states depended spaces. Moreover, we construct two orthogonal sets in general multipartite quantum systems which are locally stable under every bipartition of the subsystems. As a consequence, we obtain a lower bound and an upper bound on the size of the smallest set which is locally stable for each bipartition of the subsystems. Our results provide a complete answer to an open question (that is, can we show strong quantum nonlocality in $\mathbb{C}^{d_1} \otimes \mathbb{C}^{d_1}\otimes \cdots \otimes \mathbb{C}^{d_N} $ for any $d_i \geq 2$ and $1\leq i\leq N$?) raised in a recent paper [\href{https://journals.aps.org/pra/abstract/10.1103/PhysRevA.105.022209}{Phys. Rev. A \textbf{105}, 022209 (2022)}]. Compared with all previous relevant proofs, our proof here is quite concise.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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