Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing

2015/04/27 by Cédric Bamps, Stefano Pironio · 17 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1103/physreva.91.052111

published as Phys. Rev. A 91, 052111 (2015) · 14 pages, 3 figures

arxiv created 2015/04/27 · openalex publication_date 2015/05/19 · arxiv updated 2015/05/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

We introduce two families of sum-of-squares (SOS) decompositions for the Bell operators associated with the tilted CHSH expressions introduced in 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 Phys. Rev. A 87, 050102 (2013), where we identify and correct two non-trivial flaws.

Citations

• Symmetry groups, semidefinite programs, and sums of squares

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