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arXiv · 2002.12216

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

Debashis Saha·Rafael Santos·Remigiusz Augusiak
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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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Debashis Saha, Rafael Santos, Remigiusz Augusiak. 2022-03-04. Sum-of-squares decompositions for a family of noncontextuality inequalities and self-testing of quantum devices. https://doi.org/10.22331/q-2020-08-03-302

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