Three-Qubit-Embedded Split Cayley Hexagon is Contextuality Sensitive

• URL: http://arxiv.org/abs/2202.00726v1
• Date: Tue, 1 Feb 2022 19:53:27 GMT
• Title: Three-Qubit-Embedded Split Cayley Hexagon is Contextuality Sensitive
• Authors: Fr\'ed\'eric Holweck, Henri de Boutray and Metod Saniga
• Abstract summary: It is known that there are two non-equivalent embeddings of the split Cayley hexagon of order two into $mathcalW(5,2)$, the binary symplectic polar space of rank three. We show that the complement of a classically-embedded hexagon is not contextual, whereas that of a skewly-embedded one is.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: It is known that there are two non-equivalent embeddings of the split Cayley hexagon of order two into $\mathcal{W}(5,2)$, the binary symplectic polar space of rank three, called classical and skew. Labelling the 63 points of $\mathcal{W}(5,2)$ by the 63 canonical observables of the three-qubit Pauli group subject to the symplectic polarity induced by the (commutation relations between the elements of the) group, the two types of embedding are found to be quantum contextuality sensitive. In particular, we show that the complement of a classically-embedded hexagon is not contextual, whereas that of a skewly-embedded one is.

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