AUTHOR=Bai Lihua , Xiao Shu , Guo Zhihua , Cao Huaixin 

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

JOURNAL=Frontiers in Physics

VOLUME=10

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.864452

DOI=10.3389/fphy.2022.864452

ISSN=2296-424X

ABSTRACT=<p>When an <italic>n</italic>-partite physical system is measured by <italic>n</italic> observers, the joint probabilities of outcomes conditioned on the observables chosen by the <italic>n</italic> parties form a nonnegative tensor, called an <italic>n</italic>-partite correlation tensor (CT). In this paper, we aim to establish some characterizations of nonsignaling and Bell locality of an <italic>n</italic>-partite CT, respectively. By placing CTs within the linear space of correlation-type tensors (CTTs), we prove that every <italic>n</italic>-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 <italic>n</italic>-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 <italic>n</italic>-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.</p>