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.
Highlights
Violation of a noncontextuality inequality or the phenomenon referred to ‘quantum contextuality’ is a fundamental feature of quantum theory
It poses a fundamental question: presuming the minimum features of the devices how to characterize (i) quantum systems of prime dimension that are not capable of exhibiting nonlocal correlations, and (ii) quantum systems without entanglement or spatial separation between subsystems? A possible way to address such instances is to employ quantum contextuality (KochenSpecker contextuality), a generalization of nonlocal correlations obtained from the statistics of commuting measurements that are performed on a single quantum sys
Kochen-Specker contextuality captures the intrinsic nature of quantum theory that essentially departs from classicality
Summary
We begin by illustrating our scenario and specifying the assumptions. Sequential-measurement set-up. The measurement device only returns the actual post-measurement state This assumption is necessary, otherwise, any quantum statistics can be reproduced by classical systems. Kochen-Specker contextuality [CSW14] pertains to the following assumptions: (i) the measurements are projective, that is, Ki, Ki are projectors, and (ii) the projectors satisfy certain orthogonality relations, in this scenario, FiFi±1 = 0 for all i, implying [Ai, Ai±1] = 0. Such prerequisites about the measurement device are difficult to justify in practice. Our SOS is designed in such a way that the algebraic relations (14) it implies can be used for selftesting
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