论文标题
具有特殊量子非局部性的最小量子状态的界限
Bounds on the smallest sets of quantum states with special quantum nonlocality
论文作者
论文摘要
如果在子系统的每两分部分\ href {https://journals.aps.org/prl/prl/10.110.110.1103/physrevlett.122.04040404040404040404040404040404040404040404040404040404040404040404040404040404040404040404040404040404040404040404040年，在多部分系统中的一组正交状态被称为强量子非局部性。莱特牧师。 \ textbf {122}，040403（2019）}]。在这项工作中，我们研究了本地不可约集的子类：每个子系统上唯一可能的正交性测量是琐碎的测量。我们将此属性称为本地稳定。我们发现，在两个量子位系统的情况下，本地稳定的集合与本地不可分割的集合一致。然后，我们通过某些状态依赖空间的维度提出了局部稳定集的表征。此外，我们在一般的多部分量子系统中构造了两个正交集，它们在子系统的每个两者下都是局部稳定的。结果，我们获得了最小集合大小的下限和上限，该集合的大小是局部稳定的，对于子系统的每个两十字架而言。 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 $？）在最近的论文[\ href {https://journals.aps.org/pra/abstra/10.1103/physreva.105.022209} {phys {phys。修订版A \ textbf {105}，022209（2022）}]。与所有以前的相关证明相比，我们在这里的证明非常简洁。
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.
