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

Debashis Saha, Rafael Santos, and Remigiusz Augusiak

Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland

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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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Cited by

[1] Owidiusz Makuta and Remigiusz Augusiak, "Self-testing maximally-dimensional genuinely entangled subspaces within the stabilizer formalism", New Journal of Physics 23 4, 043042 (2021).

[2] Li-Yi Hsu and Ching-Hsu Chen, "Exploring Bell nonlocality of quantum networks with stabilizing and logical operators", Physical Review Research 3 2, 023139 (2021).

[3] Debarshi Das, Ananda G. Maity, Debashis Saha, and A. S. Majumdar, "Robust certification of arbitrary outcome quantum measurements from temporal correlations", Quantum 6, 716 (2022).

[4] Rafael Santos, Chellasamy Jebarathinam, and Remigiusz Augusiak, "Scalable noncontextuality inequalities and certification of multiqubit quantum systems", Physical Review A 106 1, 012431 (2022).

[5] Ananda G. Maity, Shiladitya Mal, Chellasamy Jebarathinam, and A. S. Majumdar, "Self-testing of binary Pauli measurements requiring neither entanglement nor any dimensional restriction", Physical Review A 103 6, 062604 (2021).

[6] Adel Sohbi, Damian Markham, Jaewan Kim, and Marco Túlio Quintino, "Certifying dimension of quantum systems by sequential projective measurements", Quantum 5, 472 (2021).

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