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Multiple Qubits as Symplectic Polar Spaces of Order Two

Metod Saniga·Michel Planat
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Abstract

It is surmised that the algebra of the Pauli operators on the Hilbert space of N-qubits is embodied in the geometry of the symplectic polar space of rank N and order two, W_{2N - 1}(2). The operators (discarding the identity) answer to the points of W_{2N - 1}(2), their partitionings into maximally commuting subsets correspond to spreads of the space, a maximally commuting subset has its representative in a maximal totally isotropic subspace of W_{2N - 1}(2) and, finally, "commuting" translates into "collinear" (or "perpendicular").

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Metod Saniga, Michel Planat. 2006-12-21. Multiple Qubits as Symplectic Polar Spaces of Order Two. https://arxiv.org/abs/quant-ph/0612179

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