Discrete phase-space structure of -qubit mutually unbiased bases
arXiv:0806.0726 · doi:10.1016/j.aop.2008.10.003
Abstract
We work out the phase-space structure for a system of qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field $\Gal{2^n}$ and investigate 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 properties. We provide a simple classification of such curves and study in detail the four- and eight-dimensional cases, analyzing also the effect of local transformations. In this way, we provide a comprehensive phase-space approach to the construction of mutually unbiased bases for qubits.
Title changed. Improved version. Accepted for publication in Annals of Physics