The Veldkamp Space of Two-Qubits

Metod Saniga (1) , Michel R. P. Planat (2) , Petr Pracna (3) , Hans Havlicek (4)

1 Astronomical Institute of the Slovak Academy of Sciences
2 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
3 JH-INST - J. Heyrovsky Institute of Physical Chemistry
4 TUW - Institut fuer Diskrete Mathematik und Geometrie

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 $W(2)$.

Mots clés: Generalized Quadrangles; Veldkamp Spaces; Pauli Operators of Two-Qubits

Domaines: Physique Quantique [quant-ph]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Metod Saniga, Michel R. P. Planat, Petr Pracna, Hans Havlicek. The Veldkamp Space of Two-Qubits. SIGMA, 2007, 3, 075, 7 p. ⟨hal-00139548v3⟩