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Optimal non-signalling violations via tensor norms

  • Abderramán Amr ReyEmail author
  • Carlos Palazuelos
  • Ignacio Villanueva
Article
  • 13 Downloads

Abstract

In this paper we characterize the set of bipartite non-signalling probability distributions in terms of tensor norms. Using this characterization we give optimal upper and lower bounds on Bell inequality violations when non-signalling distributions are considered. Interestingly, our upper bounds show that non-signalling Bell inequality violations cannot be significantly larger than quantum Bell inequality violations.

Keywords

Quantum information Bell inequalities Non-signalling distributions Tensor norms 

Mathematics Subject Classification

81P45 46B28 

Notes

Acknowledgements

This research was funded by the Spanish MINECO through Grant No. MTM2017-88385-P, MTM2014-54240-P and by the Comunidad de Madrid through grant QUITEMAD-CM P2018/TCS4342. We also acknowledge funding from SEV-2015-0554-16-3 and “Ramón y Cajal program” RYC-2012-10449 (C. P.).

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Copyright information

© Universidad Complutense de Madrid 2019

Authors and Affiliations

  1. 1.Departamento de Análisis Matemático y Matemática AplicadaUniversidad Complutense de MadridMadridSpain
  2. 2.Instituto de Ciencias Matemáticas (ICMAT)MadridSpain
  3. 3.Instituto Matemáticas Interdisciplinar (IMI)Universidad Complutense de MadridMadridSpain

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