Several nonlocal sets of multipartite pure orthogonal product states

多方 量子非定域性 多体纠缠 正交性 量子纠缠 LOCC公司 数学 基础(线性代数) 产品(数学) 班级(哲学) 线性子空间 正交基 国家(计算机科学) 集合(抽象数据类型) 维数(图论) 量子态 组合数学 离散数学 量子 压扁的纠缠 纯数学 计算机科学 量子力学 物理 算法 几何学 人工智能 程序设计语言
作者
Saronath Halder
出处
期刊:Physical review [American Physical Society]
卷期号:98 (2) 被引量:76
标识
DOI:10.1103/physreva.98.022303
摘要

It is known that there exist sets of pure orthogonal product states which cannot be perfectly distinguished by local operations and classical communication (LOCC). Such sets are nonlocal sets which exhibit nonlocality without entanglement. These nonlocal sets can be completable or uncompletable. In this work both completable and uncompletable small nonlocal sets of multipartite orthogonal product states are constructed. Apart from nonlocality, these sets have other interesting properties. In particular, the completable sets lead to the construction of a class of complete orthogonal product bases with the property that if such a basis is given then no state can be eliminated from that basis by performing orthogonality-preserving measurements. On the other hand, an uncompletable set of the present kind contains several Shifts unextendible product bases (UPBs) that belong to qubit subspaces. Identifying these subspace UPBs, it is possible to obtain a class of high-dimensional multipartite bound entangled states. Finally, it is shown that a two-qubit maximally entangled Bell state shared between any two parties is sufficient as a resource to distinguish the states of any completable set (of the above kind) perfectly by LOCC. This constitutes an example where the amount of entanglement, sufficient to accomplish the aforesaid task, depends neither on the dimension of the individual subsystems nor on the number of parties.
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