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arXiv · 0806.0726

Discrete phase-space structure of $n$-qubit mutually unbiased bases

A. B. Klimov·J. L. Romero·G. Bjork·L. L. Sanchez-Soto
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Abstract

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 $\Gal{2^n}$ 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 $n$ qubits.

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A. B. Klimov, J. L. Romero, G. Bjork, L. L. Sanchez-Soto. 2008-11-17. Discrete phase-space structure of $n$-qubit mutually unbiased bases. https://doi.org/10.1016/j.aop.2008.10.003

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