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Finding all the mutually unbiased bases in various dimensions is a problem offundamental interest in quantum information theory and pure mathematics. Thegeneral problem formulated in finite-dimensional Hilbert spaces is open. In thecategorical approach to quantum mechanics one can find examples of categorieswhich behave ``like'' the category of finite-dimensional Hilbert spaces invarious ways but are subtly different. One such category is the category ofsets and relations, $\mathbf{Rel}$. One can formulate the concept of mutuallyunbiased bases here as well. In this note we classify all the mutually unbiasedbases in this category by relating it to a standard question in combinatorics.

Classifying all mutually unbiased bases in Rel