On the connection between mutually unbiased bases and orthogonal Latin squares

Understand

We offer a piece of evidence that the problems of finding the number of mutually unbiased bases (MUB) and mutually orthogonal Latin squares (MOLS) might not be equivalent.

• We study a particular procedure which has been shown to relate the two problems and generates complete sets of MUBs in power-of-prime dimensions and three MUBs in dimension six.
• For these cases, every square from an augmented set of MOLS has a corresponding MUB.
• We show that this no longer holds for certain composite dimensions.