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Multiple Qubits as Symplectic Polar Spaces of Order Two

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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Submitted on : Thursday, December 21, 2006 - 10:44:00 AM
Last modification on : Thursday, January 13, 2022 - 12:00:07 PM
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Metod Saniga, Michel R. P. Planat. Multiple Qubits as Symplectic Polar Spaces of Order Two. Advanced Studies in Theoretical Physics, 2007, 1, pp.1 - 4. ⟨hal-00121565⟩

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