Contextuality degree of quadrics in multi-qubit symplectic polar spaces

Abstract

Quantum contextuality takes an important place amongst the concepts of quantum computing that bring an advantage over its classical counterpart. For a large class of contextuality proofs, aka. observable-based proofs of the Kochen-Specker Theorem, we formulate the contextuality property as the absence of solutions to a linear system and define for a contextual configuration its degree of contextuality. Then we explain why subgeometries of binary symplectic polar spaces are candidates for contextuality proofs. We report the results of a software that generates these subgeometries, decides their contextuality and computes their contextuality degree for some small symplectic polar spaces. We show that quadrics in the symplectic polar space $W_n$ are contextual for $n=3,4,5$. The proofs we consider involve more contexts and observables than the smallest known proofs. This intermediate size property of those proofs is interesting for experimental tests, but could also be interesting in quantum game theory.

arXiv comment18 pages, 4 figures, 4 tables. Mistake in first line of Table 2 corrected

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Cited by in corpus (6)

• New and improved bounds on the contextuality degree of multi-qubit configurations
• Three-Qubit-Embedded Split Cayley Hexagon is Contextuality Sensitive
• Quantitative comparison of quantum pseudo-telepathy games and Bell inequalities
• An abstract structure determines the contextuality degree of observable-based Kochen-Specker proofs
• A new heuristic approach for contextuality degree estimates and its four- to six-qubit portrayals
• Hexagons govern three-qubit contextuality