Mutually unbiased bases for continuous variables

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



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.

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