Open AccessQuantum limit of genuine tripartite correlations by bipartite extremality
Author(s) -
Hiroyuki Ozeki,
Satoshi Ishizaka
Publication year - 2020
Publication title -
international journal of quantum information
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.268
H-Index - 41
eISSN - 1793-6918
pISSN - 0219-7499
DOI - 10.1142/s0219749920500148
Subject(s) - bipartite graph , mathematics , limit (mathematics) , quantum , quantum nonlocality , set (abstract data type) , combinatorics , chsh inequality , value (mathematics) , parameter space , statistical physics , discrete mathematics , quantum entanglement , physics , quantum mechanics , statistics , mathematical analysis , computer science , graph , programming language
The characterization of the extremal points of the set of quantum correlations has attracted wide interest. In the simplest bipartite Bell scenario, a necessary and sufficient criterion for identifying extremal correlations has recently been conjectured, but extremality of tripartite correlations is not well known. In this study, we analyze tripartite extremal correlations in terms of the conjectured bipartite extremal criterion, and we demonstrate that the bipartite part of some extremal correlations satisfies the bipartite criterion, even though they violate Svetlichny’s inequality, and therefore are considered (stronger) genuine tripartite nonlocal correlations. This phenomenon arises from the fact that the conjectured extremal criterion is automatically satisfied when the violation of the Clauser–Horne–Shimony–Holt (CHSH) inequality exceeds a certain threshold, the value of which is given by the maximum CHSH violation at the edges of the probability space. This also suggests the possibility that the extremality of bipartite correlations can be certified by verifying whether the CHSH violation exceeds the threshold.