Bell non-locality using tensor networks and sparse recovery

• URL: http://arxiv.org/abs/2001.11455v2
• Date: Fri, 31 Jan 2020 14:17:09 GMT
• Title: Bell non-locality using tensor networks and sparse recovery
• Authors: I. S. Eli\"ens and S. G. A. Brito and R. Chaves
• Abstract summary: Bell's theorem, stating that quantum predictions are incompatible with a local hidden variable description, is a cornerstone of quantum theory. We propose to analyse a Bell scenario as a tensor network, a perspective permitting to test and quantify non-locality. It allows to prove that non-signalling correlations can be described by hidden variable models governed by a quasi-probability.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bell's theorem, stating that quantum predictions are incompatible with a local hidden variable description, is a cornerstone of quantum theory and at the center of many quantum information processing protocols. Over the years, different perspectives on non-locality have been put forward as well as different ways to to detect non-locality and quantify it. Unfortunately and in spite of its relevance, as the complexity of the Bell scenario increases, deciding whether a given observed correlation is non-local becomes computationally intractable. Here, we propose to analyse a Bell scenario as a tensor network, a perspective permitting to test and quantify non-locality resorting to very efficient algorithms originating from compressed sensing and that offer a significant speedup in comparison with standard linear programming methods. Furthermore, it allows to prove that non-signalling correlations can be described by hidden variable models governed by a quasi-probability.

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