Multiple Qubits as Symplectic Polar Spaces of Order Two

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, W2N−1(2). The operators (discarding the identity) answer to the points of W2N−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 W2N−1(2) and, finally, “commuting” translates into “collinear” (or “perpendicular”). Mathematics Subject Classification: 51Exx, 81R99