论文标题
在平面结构上具有强量子非局部性的正交产品集
Orthogonal product sets with strong quantum nonlocality on plane structure
论文作者
论文摘要
在本文中，我们考虑具有强量子非局部性的正交产品集（OPS）。基于平面几何形状的分解，我们为在固定子系统上具有正交性POVM的微不足道提供了足够的条件，并部分回答了Yuan等人给出的一个空旷的问题。物理。修订版A \ textbf {102}，042228（2020）}。建立了非局部性与平面结构之间的连接。我们成功地在$ \ Mathcal {C}^{d_ {d_ {a}} \ otimes \ Mathcal {C}^{d_ {d_ {b}} \ otimes \ Mathcal \ Mathcal {c}^{c}^{d_ {量子状态，并将已知OPS的结构推广到任何可能的三个和四方系统。此外，我们还提出了几种纠缠辅助协议，以完全局部歧视集合。结果表明，没有传送的协议平均使用较少的纠缠资源，并且这些集合总是可以在本地歧视的，该集合可以在本地区分多个副本的最大纠缠状态的多个副本。这些结果在量子状态的局部歧视中也表现出最大纠缠状态的非平凡含义。
In this paper, we consider the orthogonal product set (OPS) with strong quantum nonlocality. Based on the decomposition of plane geometry, we present a sufficient condition for the triviality of orthogonality-preserving POVM on fixed subsystem and partially answer an open question given by Yuan et al. Phys. Rev. A \textbf{102}, 042228 (2020)}. The connection between the nonlocality and the plane structure of OPS is established. We successfully construct a strongly nonlocal OPS in $\mathcal{C}^{d_{A}}\otimes \mathcal{C}^{d_{B}}\otimes \mathcal{C}^{d_{C}}$ $(d_{A,B,C}\geq 4)$, which contains fewer quantum states, and generalize the structures of known OPSs to any possible three and four-partite systems. In addition, we present several entanglement-assisted protocols for perfectly local discrimination the sets. It is shown that the protocols without teleportation use less entanglement resources on average and these sets can always be discriminated locally with multiple copies of 2-qubit maximally entangled states. These results also exhibit nontrivial signification of maximally entangled states in the local discrimination of quantum states.
