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

Résumé : 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

hal-00002833, version 3
http://hal.archives-ouvertes.fr/hal-00002833
oai:hal.archives-ouvertes.fr:hal-00002833
Contributeur : Michel Planat <>
Soumis le : Jeudi 12 Octobre 2006, 10:47:34
Dernière modification le : Vendredi 26 Janvier 2007, 09:24:08

Voir la fiche détaillée

Documents associés

PS :

PDF :

arXiv : quant-ph/0409081

Exporter

Bibtex EndNote TEI RefWorks

<?xml version="1.0" encoding="UTF-8"?>
<listBibl xmlns="http://www.tei-c.org/ns/1.0" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<listBibl type="article"><head>Articles dans des revues avec comité de lecture</head>
<biblStruct type="article" xml:id="hal-00002833"><analytic>
<author><persName><forename>Michel</forename><surname>Planat</surname></persName>
<affiliation>
<orgName type="laboratory">FEMTO-ST</orgName>
<orgName type="team">Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies</orgName>
<country>FR</country>
<orgName type="institution">CNRS : UMR6174</orgName>
<orgName type="institution">Université de Franche-Comté</orgName>
<orgName type="institution">Université de Technologie de Belfort-Montbeliard</orgName>
<orgName type="institution">Ecole Nationale Supérieure de Mécanique et des Microtechniques</orgName>
</affiliation>
</author>
<author><persName><forename>Haret</forename><surname>Rosu</surname></persName>
<affiliation>
<orgName type="team">Dept of Applied Mathematics</orgName>
<country>MX</country>
<orgName type="institution">IPICyT</orgName>
</affiliation>
</author>
<author><persName><forename>Serge</forename><surname>Perrine</surname></persName>
<affiliation>
<orgName type="laboratory">FT R&D</orgName>
<orgName type="team">France Télécom Recherche & Développement</orgName>
<country>FR</country>
<orgName type="institution">France Télécom</orgName>
</affiliation>
</author>
<author><persName><forename>Metod</forename><surname>Saniga</surname></persName>
<affiliation>
<orgName type="team">Astronomical Institute</orgName>
<country>CZ</country>
<orgName type="institution">Slovak Academy of Sciences</orgName>
</affiliation>
</author>
<title type="main" level="a">A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements</title></analytic><monogr><title level="j" type="main">Foundations of Physics</title><imprint><biblScope type="publicationDate">2006-00-00</biblScope><biblScope type="vol">36</biblScope><biblScope type="pp">1662-1680</biblScope></imprint></monogr><idno type="HALid">http://hal.archives-ouvertes.fr/hal-00002833</idno><idno type="HALFile">http://hal.archives-ouvertes.fr/hal-00002833/PDF/MUB_FP1-ED.pdf</idno></biblStruct>
</listBibl>
</listBibl>