  The goal of these notes is to show that the classification problem of
algebraically unbiased system of projectors has an interpretation in symplectic
geometry. This leads us to a description of the moduli space of algebraically
unbiased bases as critical points of a potential functions, which is a Laurent
polynomial in suitable coordinates. The Newton polytope of the Laurent
polynomial is the classical Birkhoff polytope, the set of double stochastic
matrices. Mirror symmetry interprets the polynomial as a Landau-Ginzburg
potential for corresponding Fano variety and relates the symplectic geometry of
the variety with systems of unbiased projectors.
