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

2015/05/19 by Cédric Bamps, Stefano Pironio · 6 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications

paper · doi:10.1103/physreva.91.052111

openalex publication_date 2015/05/19 · 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 Clauser-Horne-Shimony-Holt (CHSH) expressions introduced in Ac'\in 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 Navascu'es [Phys. Rev. A 87, 050102(R) (2013)], where we identify and correct two nontrivial flaws.

Citations

• Symmetry groups, semidefinite programs, and sums of squares

Cited by

• Computational Bell Inequalities
• Experimental self-testing of entangled states
• Communication scenario enables robust self-testing of n-party Greenberger-Horne-Zeilinger basis measurements
• Any gate of a quantum computer can be certified device-independently
• Robust Self-Testing of Multiqudit Supersinglet Slater States via Constant Number of Binary Measurements
• Robustly self-testing all maximally entangled states in every finite dimension

Related

• Self-testing in the compiled setting via tilted-CHSH inequalities
• Variant of the Clauser-Horne-Shimony-Holt inequality
• Maximal violation of Clauser-Horne-Shimony-Holt inequality for two qutrits
• On the equivalence of the CH and CHSH inequalities for two three-level systems
• The Clauser-Horne-Shimony-Holt inequality in the context of a broad random variable