论文标题
相关张量的双重性和$ n $ loclocality的特征
Characterizations of bilocality and $n$-locality of correlation tensors
论文作者
论文摘要
在文献中，相关张量（CTS）的双端口性和$ n $ - 局部性通过集成局部隐藏变量模型（称为C-LHVM）而不是通过Sumpation LHVM（称为D-LHVM）来描述。显然，与D-LHVM相比，C-LHVM更容易构造，而后者比前者更容易使用，例如，在讨论所有bilocal和所有$ n $ local-local cts的拓扑和几何特性时。在这种情况下，可以询问这两个描述是否等效。在目前的工作中，我们首先建立了三方CT $ {\ bf {p}} = \ lbrack P（abc | xyz）\ rbrack $的双分支ct $ {\ bf {p}} = \ rbrack $的等效特征，这意味着双重性的两个描述相当于。作为应用程序，我们证明所有具有相同尺寸的Bilocal CT形成一个紧凑的路径连接集，该集合具有许多Star-Convex子集。其次，我们介绍和讨论三方概率张量（PT）$ {\ bf {p}} = \ lbrack p（abc）\ rbrack $的双分裂性，包括同等的特征和双向pts的属性。最后，我们获得有关$ n+1 $ -1 $ -partite cts $ {\ bf {\ bf {p}} = \ lbrack p（{\ bf {a}} b | {\ bf | {\ bf {x}} y） p（{\ bf {a}} b）\ rbrack $。
In the literature, bilocality and $n$-locality of correlation tensors (CTs) are described by integration local hidden variable models (called C-LHVMs) rather than by summation LHVMs (called D-LHVMs). Obviously, C-LHVMs are easier to be constructed than D-LHVMs, while the later are easier to be used than the former, e.g., in discussing on the topological and geometric properties of the sets of all bilocal and of all $n$-local CTs. In this context, one may ask whether the two descriptions are equivalent. In the present work, we first establish some equivalent characterizations of bilocality of a tripartite CT ${\bf{P}}=\Lbrack P(abc|xyz)\Rbrack$, implying that the two descriptions of bilocality are equivalent. As applications, we prove that all bilocal CTs with the same size form a compact path-connected set that has many star-convex subsets. Secondly, we introduce and discuss the bilocality of a tripartite probability tensor (PT) ${\bf{P}}=\Lbrack P(abc)\Rbrack$, including equivalent characterizations and properties of bilocal PTs. Lastly, we obtain corresponding results about $n$-locality of $n+1$-partite CTs ${\bf{P}}=\Lbrack P({\bf{a}}b|{\bf{x}}y)\Rbrack$ and PTs ${\bf{P}}=\Lbrack P({\bf{a}}b)\Rbrack$, respectively.
