Bounding the Set of Quantum Correlations

Miguel Navascués, Stefano Pironio, and Antonio Acín
Phys. Rev. Lett. 98, 010401 – Published 4 January 2007

Abstract

We introduce a hierarchy of conditions necessarily satisfied by any distribution Pαβ representing the probabilities for two separate observers to obtain outcomes α and β when making local measurements on a shared quantum state. Each condition in this hierarchy is formulated as a semidefinite program. Among other applications, our approach can be used to obtain upper bounds on the quantum violation of an arbitrary Bell inequality. It yields, for instance, tight bounds for the violations of the Collins et al. inequalities.

  • Received 18 July 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.010401

©2007 American Physical Society

Authors & Affiliations

Miguel Navascués*, Stefano Pironio, and Antonio Acín

  • ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain

  • *Electronic address: Miguel.Navascues@icfo.es
  • Electronic address: Stefano.Pironio@icfo.es
  • Electronic address: Antonio.Acin@icfo.es

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Issue

Vol. 98, Iss. 1 — 5 January 2007

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