Contextuality degree of quadrics in multi-qubit symplectic polar spaces

TL;DR

This paper investigates the degree of quantum contextuality in quadrics within multi-qubit symplectic polar spaces, introducing a new measure and computational approach to analyze their contextuality properties.

Contribution

It formulates the contextuality degree as the absence of solutions to linear systems and applies this to subgeometries of symplectic polar spaces, providing new insights into their contextuality.

Findings

Quadrics in $W_n$ are contextual for n=3,4,5.

Generated subgeometries show more contexts and observables than minimal proofs.

Results are relevant for experimental tests and quantum game theory.

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.