Decompositions of n-Partite Nonsignaling Correlation-Type Tensors With Applications

被引:9
|
作者
Bai, Lihua
Xiao, Shu
Guo, Zhihua
Cao, Huaixin
机构
[1] School of Mathematics and Statistics, Shaanxi Normal University, Xi’an
基金
中国国家自然科学基金;
关键词
nonsignaling; Bell locality; correlation tensor; correlation-type tensor; Bell nonlocality; NONLOCALITY; INEQUALITIES; THEOREM;
D O I
10.3389/fphy.2022.864452
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
When an n-partite physical system is measured by n observers, the joint probabilities of outcomes conditioned on the observables chosen by the n parties form a nonnegative tensor, called an n-partite correlation tensor (CT). In this paper, we aim to establish some characterizations of nonsignaling and Bell locality of an n-partite CT, respectively. By placing CTs within the linear space of correlation-type tensors (CTTs), we prove that every n-partite nonsignaling CTT can be decomposed as a linear combination of all local deterministic CTs using single-value decomposition of matrices and mathematical induction. As a consequence, we prove that an n-partite CT is nonsignaling (resp. Bell local) if and only if it can be written as a quasi-convex (resp. convex) combination of the outer products of deterministic CTs, implying that an n-partite CT is nonsignaling if and only if it has a local hidden variable model governed by a quasi-probability distribution. As an application of these results, we prove that a CT is nonsignaling if and only if it can be written as a quasi-convex of two Bell local ones, revealing a close relationship between nonsignaling CTs and Bell local ones.
引用
收藏
页数:10
相关论文
empty
未找到相关数据