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

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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.

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Authors and Affiliations

  1. Institut FEMTO-ST Departement LPMO, 32 Avenue de l’Observatoire, 25044, Besançon Cedex, France

    Michel Planat

  2. Potosinian Institute of Science and Technology (IPICyT), Apdo Postal 3-74 Tangamanga, 78231, San Luis Potosí, S.L.P., Mexico

    Haret C. Rosu

  3. France Telecom, Conseil Scientifique, 38-40 rue du Général Leclerc, 92794, Issy les Moulineaux Cedex 9, France

    Serge Perrine

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  1. Michel Planat
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  2. Haret C. Rosu
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  3. Serge Perrine
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Correspondence to Haret C. Rosu.

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Planat, M., Rosu, H.C. & Perrine, S. A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements. Found Phys 36, 1662–1680 (2006). https://doi.org/10.1007/s10701-006-9079-3

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  • DOI: https://doi.org/10.1007/s10701-006-9079-3

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