Discrete Phase-Space Structures and Mutually Unbiased Bases

Authors:
A. B. Klimov;J. L. Romero;G. Björk;L. L. Sánchez-Soto
Affiliations:
Departamento de Física, Universidad de Guadalajara, Revolución 1500, 44420 Guadalajara, Jalisco, Mexico;Departamento de Física, Universidad de Guadalajara, Revolución 1500, 44420 Guadalajara, Jalisco, Mexico;School of Information and Communication Technology, Royal Institute of Technology (KTH), Electrum 229, SE-164 40 Kista, Sweden;Departamento de Óptica, Facultad de Física, Universidad Complutense, 28040 Madrid, Spain
Venue:
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Year:
2007

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Abstract

We propose a unifying phase-space approach to the construction of mutually unbiased bases for an n-qubit system. It is based on an explicit classification of the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional conditions. The effect of local transformations is also studied.