caa a22 4500 467906696 CHVBK 20180406152836.0 cr unu---uuuuu 170328e20061101xx s 000 0 eng 10.1007/s10701-006-9079-3 doi (NATIONALLICENCE)springer-10.1007/s10701-006-9079-3 A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements [Elektronische Daten] [Michel Planat, Haret Rosu, Serge Perrine] The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are reviewed 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. Springer Science+Business Media, LLC, 2006 mutually unbiased bases nationallicence d -dimensional Hilbert space nationallicence Galois fields and rings nationallicence maximally entangled states nationallicence Planat Michel Institut FEMTO-ST Departement LPMO, 32 Avenue de l'Observatoire, 25044, Besançon Cedex, France aut Rosu Haret Potosinian Institute of Science and Technology (IPICyT), Apdo Postal 3-74 Tangamanga, 78231, San Luis Potosí, S.L.P., Mexico aut Perrine Serge France Telecom, Conseil Scientifique, 38-40 rue du Général Leclerc, 92794, Issy les Moulineaux Cedex 9, France aut Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/11(2006-11-01), 1662-1680 0015-9018 36:11<1662 2006 36 10701 https://doi.org/10.1007/s10701-006-9079-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10701-006-9079-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Planat Michel Institut FEMTO-ST Departement LPMO, 32 Avenue de l'Observatoire, 25044, Besançon Cedex, France aut NATIONALLICENCE 700 1- Rosu Haret Potosinian Institute of Science and Technology (IPICyT), Apdo Postal 3-74 Tangamanga, 78231, San Luis Potosí, S.L.P., Mexico aut NATIONALLICENCE 700 1- Perrine Serge France Telecom, Conseil Scientifique, 38-40 rue du Général Leclerc, 92794, Issy les Moulineaux Cedex 9, France aut NATIONALLICENCE 773 0- Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/11(2006-11-01), 1662-1680 0015-9018 36:11<1662 2006 36 10701 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer