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

Journal Article · Tue Oct 15 00:00:00 EDT 2013 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/J.AOP.2013.06.018· OSTI ID:22224220

Shalaby, M.

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 d{sub i} points where d{sub i}|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). -- Highlights: •Lines in discrete phase space. •Bases in finite quantum systems. •Duality between bases and lines. •Weak mutually unbiased bases.

• OSTI ID: 22224220
• Journal Information: Annals of Physics (New York), Vol. 337; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DUALITY
ORIGIN
PHASE SPACE
QUANTUM MECHANICS