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arXiv · 1612.09000

An application of positive definite functions to the problem of MUBs

Mihail N. Kolountzakis·Máté Matolcsi·Mihály Weiner
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Abstract

We present a new approach to the problem of mutually unbiased bases (MUBs), based on positive definite functions on the unitary group. The method provides a new proof of the fact that there are at most $d+1$ MUBs in ${\mathbb C}^d$. It may also lead to a proof of non-existence of complete systems of MUBs in dimension 6 via a conjectured algebraic identity.

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Mihail N. Kolountzakis, Máté Matolcsi, Mihály Weiner. 2016-12-28. An application of positive definite functions to the problem of MUBs. https://arxiv.org/abs/1612.09000

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