On the mathematical foundations of mutually unbiased bases

Abstract

In order to describe the right setting to handle Zauner's conjecture on mutually unbiased bases (MUBs) (saying that in ${\mathbb{C}}^d$, a set of MUBs of the theoretical maximal size $d+1$ exists only if $d$ is a prime power), we pose some fundamental questions which naturally arise. Some of these questions have important consequences for the construction theory of (new) sets of maximal MUBs.

6 pages; submitted (September 2014)

References in corpus (1)

• Unextendible mutually unbiased bases (after Mandayam, Bandyopadhyay, Grassl and Wootters)