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arXiv · 1404.3831

Exploring non-signalling polytopes with negative probability

G. Oas·J. Acacio de Barros·C. Carvalhaes
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Abstract

Bipartite and tripartite EPR-Bell type systems are examined via joint quasi-probability distributions where elementary probabilities are permitted to be negative. It is shown that such distributions exist only when the no-signalling condition is satisfied. A characteristic measure, the probability mass, is introduced and, via its minimization, limits the number of quasi-distributions describing a given marginal probability distribution. The minimized probability mass is shown to be an alternative way to characterize non-local systems. Non-signalling polytopes for two, three, and four settings in the bipartite scenario are examined and compared to prior work. Examining perfect cloning of non-local systems within the tripartite scenario suggests defining two categories of signalling. It is seen that many properties of non-local systems can be efficiently described by quasi-probability theory.

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G. Oas, J. Acacio de Barros, C. Carvalhaes. 2014-07-05. Exploring non-signalling polytopes with negative probability. https://doi.org/10.1088/0031-8949%2F2014%2Ft163%2F014034

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