A Fourier analytic approach to the problem of mutually unbiased bases

Mate Matolcsi

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arXiv · 1009.2407

A Fourier analytic approach to the problem of mutually unbiased bases

Mate Matolcsi

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Abstract

We give an entirely new approach to the problem of mutually unbiased bases (MUBs), based on a Fourier analytic technique in additive combinatorics. The method provides a short and elegant generalization of the fact that there are at most $d+1$ MUBs in $\Co^d$. It may also yield a proof that no complete system of MUBs exists in some composite dimensions -- a long standing open problem.

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Mate Matolcsi. 2010-09-13. A Fourier analytic approach to the problem of mutually unbiased bases. https://arxiv.org/abs/1009.2407

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