On the no-signaling approach to quantum nonlocality

Abstract

The no-signaling approach to nonlocality deals with separable and inseparable multiparty correlations in the same set of probability states without conflicting causality. The set of half-spaces describing the polytope of no-signaling probability states that are admitted by the most general class of Bell scenarios is formulated in full detail. An algorithm for determining the skeleton that solves the no-signaling description is developed upon a new strategy that is partially pivoting and partially incremental. The algorithm is formulated rigorously and its implementation is shown to be effective to deal with the highly degenerate no-signaling descriptions. Several applications of the algorithm as a tool for the study of quantum nonlocality are mentioned. Applied to a large set of bipartite Bell scenarios, we found that the corresponding no-signaling polytopes have a striking high degeneracy that grows up exponentially with the size of the Bell scenario.

Two-Qubit Pure Entanglement as Optimal Social Welfare Resource in Bayesian Game

“…To establish our result, i.e, superlative behavior of all 2-qubit pure entangled states in the above described games, first we consider the set of most general 2party-2-input-2-output no-signaling (NS) correlations that constitutes a polytope, say P NS . The correlations resided in P NS have been extensively studied [29][30][31][32][33]. Any such correlation…”

Maximally nonlocal Clauser-Horne-Shimony-Holt scenarios

“…They equally apply to decompose quantum correlations into local and nonlocal parts and to identify the necessary elementary resources for mixed states in any finite multi-party scenario. A hard task we foresee is the construction of the skeleton of the degenerate no-signaling polytope 22 . An algorithm to alleviate the degeneracy problem was provided in 10 .…”

An algorithm for constructing the skeleton graph of degenerate systems of linear inequalities

“…The no-signaling and non-negativity constraints on correlations [7] produce the system of linear inequalities in Table 1. The feasible polytope P NS is the intersection of m = 24 half-spaces in an Euclidean space of dimension n = 14.…”

“…Mathematical modeling in areas of science such as the physics of quantum nonlocality [ 1 – 7 ] and systems biology [ 8 – 11 ], frequently take the form of a system of linear inequalities in some Euclidean space. Every inequality in the system defines a half-space and the intersection of all half-spaces constitutes the polyhedral feasible region of the model.…”

“…Every inequality in the system defines a half-space and the intersection of all half-spaces constitutes the polyhedral feasible region of the model. In physics, the no-signaling approach to quantum nonlocality [ 2 – 4 , 7 ] leads to degenerate systems of linear constraints for the correlations between the parties playing in a correlational set up [ 4 , 6 , 7 ]. In systems biology, the structural analysis approach for the mathematical modeling of a biological complex applies constraint-based methods that take the form of degenerate linear systems of inequalities [ 8 – 11 ].…”