On the no-signaling approach to quantum nonlocality

Méndez, José M.; Urı́as, Jesús

doi:10.1063/1.4914336

Cited by 8 publications

(13 citation statements)

References 22 publications

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“…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…”

Section: Resultsmentioning

confidence: 99%

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

Banik

Bhattacharya

Ganguly

et al. 2019

Quantum

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Entanglement is of paramount importance in quantum information theory. Its supremacy over classical correlations has been demonstrated in a numerous information theoretic protocols. Here we study possible adequacy of quantum entanglement in Bayesian game theory, particularly in social welfare solution (SWS), a strategy which the players follow to maximize sum of their payoffs. Given a multi-partite quantum state as an advice, players can come up with several correlated strategies by performing local measurements on their parts of the quantum state. A quantum strategy is called quantum-SWS if it is advantageous over a classical equilibrium (CE) strategy in the sense that none of the players has to sacrifice their CE-payoff rather some have incentive and at the same time it maximizes sum of all players' payoffs over all possible quantum advantageous strategies. Quantum state yielding such a quantum-SWS is called a quantum social welfare advice (SWA). We show that any two-qubit pure entangled states, even if it is arbitrarily close to a product state, can serve as quantum-SWA in some Bayesian game. Our result, thus, gives cognizance to the fact that every two-qubit pure entanglement is the best resource for some operational task.

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Section: Resultsmentioning

confidence: 99%

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

Banik

Bhattacharya

Ganguly

et al. 2019

Quantum

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“…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 .…”

Section: Discussionmentioning

confidence: 99%

Maximally nonlocal Clauser-Horne-Shimony-Holt scenarios

Urı́as

Martínez

2018

Sci Rep

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The key feature in correlations established by multi-party quantum entangled states is nonlocality. A quantity to measure the average nonlocality, distinguishing it from shared randomness and in a direct relation with no-signaling stochastic processes (which provide an operational interpretation of quantum correlations, without involving information transmission between the parties as to sustain causality), is proposed and resolved exhaustively for the quantum correlations established by a Clauser-Horne-Shimony-Holt setup (or CHSH box). The amount of nonlocality that is available in a CHSH box is measured by its proximity to the nearest Popescu-Rohrlich set of causal stochastic processes (aka a PR box) in the no-signaling polytope, related by polyhedral duality to Bell’s correlation function. The proposed amount of average nonlocality is an entanglement monotone with a simple relation to concurrence. We provide the optimal setup vectors of a maximally nonlocal CHSH box for any entangled pair. The strongest nonlocality is the fraction of a PR box, attained by maximally entangled qubit pairs. The most economical causal stochastic process reproducing any maximally nonlocal CHSH box is developed. Data produced by a computer implementation of the simulator agrees with the quantum mechanical formulas.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

“…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 ].…”

Section: Introductionmentioning

confidence: 99%

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

Martínez

2017

PLoS ONE

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Derive the quantitative predictions of constraint-based models require of conversion algorithms to enumerate and construct the skeleton graph conformed by the extreme points of the feasible region, where all constraints in the model are fulfilled. The conversion is problematic when the system of linear constraints is degenerate. This paper describes a conversion algorithm that combines the best of two methods: the incremental slicing of cones that defeats degeneracy and pivoting for a swift traversal of the set of extreme points. An extensive computational practice uncovers two complementary classes of conversion problems. The two classes are distinguished by a practical measure of complexity that involves the input and output sizes. Detailed characterizations of the complexity classes and the corresponding performances of the algorithm are presented. For the benefit of implementors, a simple example illustrates the stages of the exposition.

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On the no-signaling approach to quantum nonlocality

Cited by 8 publications

References 22 publications

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

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

Maximally nonlocal Clauser-Horne-Shimony-Holt scenarios

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

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