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Mutually unbiased bases for continuous variables

Weigert, Stefan and Wilkinson, Michael (2008). Mutually unbiased bases for continuous variables. Physical Review A, 78(2) 020303.

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The concept of mutually unbiased bases is studied for N pairs of continuous variables. To find mutually unbiased bases reduces, for specific states related to the Heisenberg-Weyl group, to a problem of symplectic geometry. Given a single pair of continuous variables, three mutually unbiased bases are identified while five such bases are exhibited for two pairs of continuous variables. For N=2, the golden ratio occurs in the definition of these mutually unbiased bases suggesting the relevance of number theory not only in the finite-dimensional setting.

Item Type: Journal Article
ISSN: 1050-2947
Keywords: geometry; Hilbert spaces; number theory; quantum theory
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 15744
Depositing User: Colin Smith
Date Deposited: 14 Apr 2009 15:24
Last Modified: 02 Dec 2010 20:26
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