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

Quantum systems with variables in the ring image are considered, and the concepts of weak mutually unbiased bases and mutually unbiased projectors are discussed. The lines through the origin in the image phase space, are classified into maximal lines (sets of image points), and sublines (sets of image points where image). 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).