Weigert, Stefan and Wilkinson, Michael
(2008).
*Physical Review A*, 78(2) 020303.

DOI (Digital Object Identifier) Link: | http://doi.org/10.1103/PhysRevA.78.020303 |
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Google Scholar: | Look up in Google Scholar |

## Abstract

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 |
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ISSN: | 1050-2947 |

Keywords: | geometry; Hilbert spaces; number theory; quantum theory |

Academic Unit/Department: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |

Item ID: | 15744 |

Depositing User: | Colin Smith |

Date Deposited: | 14 Apr 2009 15:24 |

Last Modified: | 04 Oct 2016 10:21 |

URI: | http://oro.open.ac.uk/id/eprint/15744 |

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