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

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

2004-09-14

arxiv.org/abs/quant-ph/0409081v3

Foundations of Physics 36 (2006) 1662-1680

Physics

Quantum Physics

20 pages, 1 figure to appear in Foundations of Physics, Nov. 2006 two more references added

Scientific paper

10.1007/s10701-006-9079-3

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.

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