Group theoretical construction of mutually unbiased bases in Hilbert spaces of prime dimensions

P. Šulc, J. Tolar

Research output: Contribution to journalArticle

25 Scopus citations

Abstract

Mutually unbiased bases in Hilbert spaces of finite dimensions are closely related to the quantal notion of complementarity. An alternative proof of existence of a maximal collection of (N + 1) mutually unbiased bases in Hilbert spaces of prime dimension N is given by exploiting the finite Heisenberg group (also called the Pauli group) and the action of on finite phase space implemented by unitary operators in the Hilbert space. Crucial for the proof is that, for prime is also a finite field.

Original languageEnglish (US)
Pages (from-to)15099-15111
Number of pages13
JournalJournal of Physics A: Mathematical and Theoretical
Volume40
Issue number50
DOIs
StatePublished - Dec 14 2007
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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