A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements
Abstract
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.
 Publication:

Foundations of Physics
 Pub Date:
 November 2006
 DOI:
 10.1007/s1070100690793
 arXiv:
 arXiv:quantph/0409081
 Bibcode:
 2006FoPh...36.1662P
 Keywords:

 Quantum Physics;
 Mathematical Physics;
 Mathematics  Mathematical Physics
 EPrint:
 20 pages, 1 figure to appear in Foundations of Physics, Nov. 2006 two more references added