Sum-of-squares decompositions for a family of noncontextuality inequalities and self-testing of quantum devices

Abstract

Violation of a noncontextuality inequality or the phenomenon referred to `quantum contextuality' is a fundamental feature of quantum theory. In this article, we derive a novel family of noncontextuality inequalities along with their sum-of-squares decompositions in the simplest (odd-cycle) sequential-measurement scenario capable to demonstrate Kochen-Specker contextuality. The sum-of-squares decompositions allow us to obtain the maximal quantum violation of these inequalities and a set of algebraic relations necessarily satisfied by any state and measurements achieving it. With their help, we prove that our inequalities can be used for self-testing of three-dimensional quantum state and measurements. Remarkably, the presented self-testing results rely on a single assumption about the measurement device that is much weaker than the assumptions considered in Kochen-Specker contextuality.

11 pages, 1 figure, an error is corrected

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• Scalable noncontextuality inequalities and certification of multiqubit quantum systems
• A computational test of quantum contextuality, and even simpler proofs of quantumness
• Contextuality of Quantum Error-Correcting Codes
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• Self-testing in a constrained prepare-measure scenario sans assuming quantum dimension
• Convexity of noncontextual wirings and how they order the set of correlations
• Certification of multi-qubit quantum systems with temporal inequalities
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• Contextuality, superlocality and nonclassicality of supernoncontextuality