A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements
Quantum Physics
2009-11-10 v3 Mathematical Physics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.quant-ph/0409081,
title = {A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements},
author = {Michel R. P. Planat and Haret Rosu and Serge Perrine and Metod Saniga},
journal= {arXiv preprint arXiv:quant-ph/0409081},
year = {2009}
}
Comments
20 pages, 1 figure to appear in Foundations of Physics, Nov. 2006 two more references added