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Lecture notes in computer science

Discrete Phase-Space Structures and Mutually Unbiased Bases

A. B. Klimov, José Luis Romero, Gunnar G. Bjork, Luis Lorenzo Sánchez-Soto

Published Sep 20, 2007• 1 citation
Publisher
DOI
10.1007/978-3-540-73074-3_26

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We work out the phase-space structure for a system of n qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field GF(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 n qubits.