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Abstract: The paper gives a short introduction to mutually unbiased bases and the Welchbounds and demonstrates that the latter is a good technical tool to explore theformer. In particular, a criterion for a system of vectors to satisfy the Welchbounds with equality is given and applied for the case of MUBs. This yields anecessary and sufficient condition on a set of orthonormal bases to form acomplete system of MUBs.This condition takes an especially elegant form in the case of homogeneoussystems of MUBs. We express some known constructions of MUBs in this form. Alsoit is shown how recently obtained results binding MUBs and some combinatorialstructures such as perfect nonlinear functions and relative difference setsnaturally follow from this criterion.Some directions for proving non-existence results are sketched as well.



Author: Aleksandrs Belovs, Juris Smotrovs

Source: https://arxiv.org/







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