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

• URL: http://arxiv.org/abs/2002.12216v3
• Date: Fri, 4 Mar 2022 12:49:20 GMT
• Title: Sum-of-squares decompositions for a family of noncontextuality inequalities and self-testing of quantum devices
• Authors: Debashis Saha, Rafael Santos, Remigiusz Augusiak
• Abstract summary: Violation of a noncontextuality inequality or the phenomenon referred to quantum contextuality' is a fundamental feature of quantum theory. We derive a novel family of noncontextuality inequalities along with their sum-of-squares decompositions. We prove that our inequalities can be used for self-testing of three-dimensional quantum state and measurements.
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• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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