The Veldkamp Space of Two-Qubits

Abstract

Given a remarkable representation of the generalized Pauli operators of two-qubits in terms of the points of the generalized quadrangle of order two, W(2), it is shown that specific subsets of these operators can also be associated with the points and lines of the four-dimensional projective space over the Galois field with two elements - the so-called Veldkamp space of W(2). An intriguing novelty is the recognition of (uni- and tri-centric) triads and specific pentads of the Pauli operators in addition to the "classical" subsets answering to geometric hyperplanes of W(2).

7 pages, 3 figures, 2 tables; Version 2 - math nomenclature fine-tuned and two references added; Version 3 - published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

References in corpus (4)

• Multiple Qubits as Symplectic Polar Spaces of Order Two
• Projective Ring Line Encompassing Two-Qubits
• The Projective Line Over the Finite Quotient Ring GF(2)[$x$]/$<x^3-x>$ and Quantum Entanglement II. The Mermin "Magic" Square/Pentagram
• Pauli graph and finite projective lines/geometries

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• Multi-Line Geometry of Qubit-Qutrit and Higher-Order Pauli Operators
• Quantum contextual finite geometries from dessins d'enfants
• Cayley-Dickson Algebras and Finite Geometry
• Taxonomy of Polar Subspaces of Multi-Qubit Symplectic Polar Spaces of Small Rank
• Contextuality degree of quadrics in multi-qubit symplectic polar spaces
• Twin "Fano-Snowflakes" Over the Smallest Ring of Ternions
• A finite geometric toy model of space-time as an error correcting code
• The Veldkamp Space of the Smallest Slim Dense Near Hexagon
• $X$-States From a Finite Geometric Perspective
• New and improved bounds on the contextuality degree of multi-qubit configurations
• 'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon
• Magic Three-Qubit Veldkamp Line and Veldkamp Space of the Doily
• Quantitative comparison of quantum pseudo-telepathy games and Bell inequalities
• A Classification of the Veldkamp Lines of the Near Hexagon L_3 times GQ(2, 2)
• Veldkamp Spaces: From (Dynkin) Diagrams to (Pauli) Groups