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Mutually unbiased projectors and duality between lines and bases in finite quantum systems

Authors
Journal
Annals of Physics
0003-4916
Publisher
Elsevier
Volume
337
Identifiers
DOI: 10.1016/j.aop.2013.06.018
Keywords
  • Finite Quantum Systems
  • Mutually Unbiased Bases

Abstract

Abstract Quantum systems with variables in the ring Z(d) are considered, and the concepts of weak mutually unbiased bases and mutually unbiased projectors are discussed. The lines through the origin in the Z(d)×Z(d) phase space, are classified into maximal lines (sets of d points), and sublines (sets of di points where di|d). The sublines are intersections of maximal lines. It is shown that there exists a duality between the properties of lines (resp., sublines), and the properties of weak mutually unbiased bases (resp., mutually unbiased projectors).

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