Classifying all mutually unbiased bases in Rel

Details Classifying all mutually unbiased bases in Rel Classifying all mutually unbiased bases in Rel

2009-09-24

arxiv.org/abs/0909.4453v2

Physics

Quantum Physics

11 pages

Scientific paper

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

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