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 (2)

• Mutually unbiased binary observable sets on N qubits
• Projective Ring Line Encompassing Two-Qubits

Cited by in corpus (27)

• Projective Ring Line of an Arbitrary Single Qudit
• Projective Ring Line Encompassing Two-Qubits
• Pauli graphs when the Hilbert space dimension contains a square: why the Dedekind psi function ?
• Factor-Group-Generated Polar Spaces and (Multi-)Qudits
• Grassmannian Connection Between Three- and Four-Qubit Observables, Mermin's Contextuality and Black Holes
• Projective Ring Line of a Specific Qudit
• Multi-Line Geometry of Qubit-Qutrit and Higher-Order Pauli Operators
• The Veldkamp Space of Two-Qubits
• Mermin's Pentagram as an Ovoid of PG(3,2)
• Qudits of composite dimension, mutually unbiased bases and projective ring geometry
• The attractor mechanism as a distillation procedure
• Five-Qubit Contextuality, Noise-Like Distribution of Distances Between Maximal Bases and Finite Geometry
• Taxonomy of Polar Subspaces of Multi-Qubit Symplectic Polar Spaces of Small Rank
• A finite geometric toy model of space-time as an error correcting code
• The Veldkamp Space of the Smallest Slim Dense Near Hexagon
• It from qubit: how to draw quantum contextuality
• Pauli graph and finite projective lines/geometries
• A Sequence of Qubit-Qudit Pauli Groups as a Nested Structure of Doilies
• $X$-States From a Finite Geometric Perspective
• A Notable Relation between $N$-Qubit and $2^{N-1}$-Qubit Pauli Groups via Binary $\mathrm{LGr}(N,2N)$
• A Finite-Geometric Classification of Three-Qubit Mermin Pentagrams
• 'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon
• A Class of Three-Qubit Contextual Configurations Located in Fano Pentads
• On sets of commuting and anticommuting Paulis
• Veldkamp Spaces: From (Dynkin) Diagrams to (Pauli) Groups
• Moebius Pairs of Simplices and Commuting Pauli Operators
• Graph States and the Variety of Principal Minors