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
共 34 条
[1]  
[Anonymous], 2009, NONNEGATIVE MATRIX T
[2]   Bell's theorem without inequalities and only two distant observers [J].
Aravind, PK .
FOUNDATIONS OF PHYSICS LETTERS, 2002, 15 (04) :397-405
[3]   Nonlocal correlations as an information-theoretic resource [J].
Barrett, J ;
Linden, N ;
Massar, S ;
Pironio, S ;
Popescu, S ;
Roberts, D .
PHYSICAL REVIEW A, 2005, 71 (02)
[4]   Maximally nonlocal and monogamous quantum correlations [J].
Barrett, Jonathan ;
Kent, Adrian ;
Pironio, Stefano .
PHYSICAL REVIEW LETTERS, 2006, 97 (17)
[5]  
Bell J. S., 1964, PHYSICS, V1, P195, DOI 10.1103/PhysicsPhysiqueFizika.1.195
[6]   Ladder proof of nonlocality without inequalities: Theoretical and experimental results [J].
Boschi, D ;
Branca, S ;
DeMartini, F ;
Hardy, L .
PHYSICAL REVIEW LETTERS, 1997, 79 (15) :2755-2758
[7]   NONLOCALITY AND GLEASON LEMMA .1. DETERMINISTIC THEORIES [J].
BROWN, HR ;
SVETLICHNY, G .
FOUNDATIONS OF PHYSICS, 1990, 20 (11) :1379-1387
[8]   Bell nonlocality [J].
Brunner, Nicolas ;
Cavalcanti, Daniel ;
Pironio, Stefano ;
Scarani, Valerio ;
Wehner, Stephanie .
REVIEWS OF MODERN PHYSICS, 2014, 86 (02) :419-478
[9]   Characterizing Bell nonlocality and EPR steering [J].
Cao, HuaiXin ;
Guo, ZhiHua .
SCIENCE CHINA-PHYSICS MECHANICS & ASTRONOMY, 2019, 62 (03)
[10]   Entropic Nonsignaling Correlations [J].
Chaves, Rafael ;
Budroni, Costantino .
PHYSICAL REVIEW LETTERS, 2016, 116 (24)