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Bell Non-Locality in Many-Body Quantum Systems with Exponential Decay of Correlations

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A Correction to this article was published on 11 January 2022

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Abstract

Using Bell inequalities as a tool to explore non-classical physical behaviours, in this paper we analyse what one can expect to find in many-body quantum physics. Concretely, framing the usual correlation scenarios as a concrete spin lattice, we want to know whether or not it is possible to violate a Bell inequality restricted to this scenario. Using clustering theorems, we are able to show that a large family of quantum many-body systems behave almost-locally, violating Bell inequalities (if so) only by a non-significant amount. We also provide examples, explain some of our assumptions via counter-examples and present all the proofs for our results. We hope the paper is self-contained.

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Acknowledgements

Many thanks to R. Rabelo for all the stimulating discussion.

Funding

This paper is a result of the Brazilian National Institute of Science and Technology on Quantum Information. This work is supported by the Brazilian agencies Conselho Nacional de Desenvolvimento Científico e Tecnológico, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, FAEPEX, and by the National Research, Development and Innovation Office of Hungary (NKFIH) through the Quantum Information National Laboratory of Hungary and through the grant FK 135220. This project/research was supported by grant number FQXi-RFP-IPW-1905 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor advised fund of Silicon Valley Community Foundation. CD was supported by a fellowship from the Grand Challenges Initiative at Chapman University.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Instituto de Matemática, Estatística e Computação Cientıfica, Universidade Estadual de Campinas, 13083-859, Campinas, São Paulo, Brazil

    Carlos H. S. Vieira & Marcelo Terra Cunha

  2. School of Physics and Astronomy, University of Leeds, LS2 9JT, Leeds, Brazil

    Cristhiano Duarte

  3. International Institute of Physics, Federal University of Rio Grande do Norte, 59070-405, Natal, Brazil

    Cristhiano Duarte

  4. Wigner Research Centre for Physics, H-1121, Budapest, Hungary

    Cristhiano Duarte

  5. Departamento de Matemática, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, 30123-970, Minas Gerais, Belo Horizonte, Brazil

    Raphael C. Drumond

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  1. Carlos H. S. Vieira
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Correspondence to Carlos H. S. Vieira.

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Vieira, C.H.S., Duarte, C., Drumond, R.C. et al. Bell Non-Locality in Many-Body Quantum Systems with Exponential Decay of Correlations. Braz J Phys 51, 1603–1616 (2021). https://doi.org/10.1007/s13538-021-00998-1

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