A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements

Michel R. P. Planat; Haret Rosu; Serge Perrine; Metod Saniga

hal-00002833, version 3

A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements

Michel R. P. Planat () ¹, Haret Rosu ², Serge Perrine ³, Metod Saniga ⁴

Foundations of Physics 36 (2006) 1662-1680

Abstract: The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of important mathematical concepts like, e.g., Fourier transforms, Galois fields and rings, finite and related projective geometries, and entanglement, to mention a few. Some applications of the theory to quantum information tasks are also mentioned.

1: Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (FEMTO-ST)
CNRS : UMR6174 – Université de Franche-Comté – Université de Technologie de Belfort-Montbeliard – Ecole Nationale Supérieure de Mécanique et des Microtechniques
2: Dept of Applied Mathematics
IPICyT
3: France Télécom Recherche & Développement (FT R&D)
France Télécom
4: Astronomical Institute
Slovak Academy of Sciences

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From: Michel Planat <>
Submitted on: Thursday, 12 October 2006 10:47:34
Updated on: Friday, 26 January 2007 09:24:08

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