Sum-of-squares decompositions for a family of Clauser-Horne-Shimony-Holt-like inequalities and their application to self-testing

Cédric Bamps and Stefano Pironio
Phys. Rev. A 91, 052111 – Published 19 May 2015

Abstract

We introduce two families of sum-of-squares (SOS) decompositions for the Bell operators associated with the tilted Clauser-Horne-Shimony-Holt (CHSH) expressions introduced in Acín et al. [Phys. Rev. Lett. 108, 100402 (2012)]. These SOS decompositions provide tight upper bounds on the maximal quantum value of these Bell expressions. Moreover, they establish algebraic relations that are necessarily satisfied by any quantum state and observables yielding the optimal quantum value. These algebraic relations are then used to show that the tilted CHSH expressions provide robust self-tests for any partially entangled two-qubit state. This application to self-testing follows closely the approach of Yang and Navascués [Phys. Rev. A 87, 050102(R) (2013)], where we identify and correct two nontrivial flaws.

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  • Received 9 January 2015

DOI:https://doi.org/10.1103/PhysRevA.91.052111

©2015 American Physical Society

Authors & Affiliations

Cédric Bamps and Stefano Pironio

  • Laboratoire d'Information Quantique, Université libre de Bruxelles (ULB), 1050 Brussels, Belgium

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Vol. 91, Iss. 5 — May 2015

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