English

An application of positive definite functions to the problem of MUBs

Quantum Physics 2016-12-30 v1

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+1d+1 MUBs in Cd{\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.

Keywords

Cite

@article{arxiv.1612.09000,
  title  = {An application of positive definite functions to the problem of MUBs},
  author = {Mihail N. Kolountzakis and Máté Matolcsi and Mihály Weiner},
  journal= {arXiv preprint arXiv:1612.09000},
  year   = {2016}
}