Detailed view

Preprint, Working Paper, ...

Available versions:

v1 (2004-09-14)

v2 (2006-06-14)

v3 (2006-10-12)

Attached file list to this document:

PS MUB_FP.ps(227.9 KB) PDF MUB_FP.pdf(252.4 KB)

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

Michel R. P. Planat1, Haret Rosu2, Serge Perrine3, Metod Saniga4

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:	FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies
2:	Dept of Applied Mathematics
3:	FT R&D - France Télécom Recherche & Développement
4:	Astronomical Institute

Keyword(s) : Finite Geometries – Galois Fields – Fourier Transforms – Quantum Information Theory

hal-00002833, version 2

http://hal.archives-ouvertes.fr/hal-00002833

oai:hal.archives-ouvertes.fr:hal-00002833

From: Michel Planat <>

Submitted on: Wednesday, 14 June 2006 09:45:44

Updated on: Wednesday, 14 June 2006 09:54:39