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").

2 pages, no figure

References in corpus (1)

• Projective Ring Line Encompassing Two-Qubits

Cited by in corpus (3)

• Projective Ring Line of an Arbitrary Single Qudit
• Projective Ring Line Encompassing Two-Qubits
• Projective Ring Line of a Specific Qudit