Contextuality in the $n$-qubit Pauli group

• URL: http://arxiv.org/abs/2608.11993v1
• Date: Wed, 12 Aug 2026 12:29:56 GMT
• Title: Contextuality in the $n$-qubit Pauli group
• Abstract summary: We introduce the notion of a noncontextual property' whose nonexistence proves the Kochen-Specker theorem.<n>For two qubits, we show that the Pauli group admits nontrivial properties, despite admitting no valuations.<n>We also perform a similar analysis for the symplectic theory underlying the $n$-qubit Pauli group.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The $n$-qubit Pauli group is an essential ingredient to most quantum applications, from computing and error correction to benchmarking and simulation. Despite comprising merely a discrete set of operators, it exhibits many quintessential features of quantum theory, including contextuality, which has been identified as a key resource to quantum advantage in a variety of different flavours. Here, we extend this analysis, introducing the notion of a `noncontextual property' whose nonexistence proves the Kochen-Specker theorem, similarly to and generalising common arguments based on the nonexistence of valuations. We relate this notion formally to the existence of Boolean-valued frame functions, and characterise all such frame functions in the case of the $n$-qubit Pauli group. For two qubits, we show that the Pauli group admits noncontextual properties, despite admitting no valuations. We then establish this as the only nontrivial such case with $n\geq 2$, by proving that any Boolean-valued frame function on stabiliser states is constant for more than two qubits. We also perform a similar analysis for the symplectic theory underlying the $n$-qubit Pauli group, for which nonconstant Boolean-valued frame functions exist for all $n$, yet only in restricted form. By comparison, this shows that contextuality in the $n$-qubit Pauli group is not only a consequence of the projective nature of the Pauli group as a representation of its underlying symplectic vector space, but of the geometry of symplectic polar spaces itself. In geometric terms, our result determines all Cameron-Liebler sets of maximal totally isotropic flats in the binary affine-symplectic space.

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