2008/02/29 by Stefan Weigert, Michael Wilkinson · 5 citations
Chemistry · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Combinatorics #Continuous variable #Discrete mathematics #Graph theory and applications #Law #Mathematics #Molecular spectroscopy and chirality #Mutually unbiased bases #Pure mathematics #Relevance (law) #Statistics #Symplectic geometry #quant-ph
paper · pdf · doi:10.1103/physreva.78.020303
published as Phys. Rev. A 78, 020303(R) (2008) · 5 pages, no figures, revised to be identical to published text
openalex publication_date 2008/08/29 · arxiv created 2008/11/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.