Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 075, 7 pages      arXiv:0704.0495

The Veldkamp Space of Two-Qubits

Metod Saniga a, Michel Planat b, Petr Pracna c and Hans Havlicek d
a) Astronomical Institute, Slovak Academy of Sciences, SK-05960 Tatranská Lomnica, Slovak Republic
b) Institut FEMTO-ST, CNRS, Département LPMO, 32 Avenue de l'Observatoire, F-25044 Besançon Cedex, France
c) J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Dolejskova 3, CZ-182 23 Prague 8, Czech Republic
d) Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8-10, A-1040 Vienna, Austria

Received April 13, 2007, in final form June 18, 2007; Published online June 29, 2007

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).

Key words: generalized quadrangles; Veldkamp spaces; Pauli operators of two-qubits.

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