  We consider the random matrix obtained by picking vectors randomly from a
large collection of mutually unbiased bases of $\mathbb{C}^n$, and prove that
the spectral distribution converges to the Marchenko-Pastur law. This shows
that vectors in mutually unbiased bases behave like random vectors. This
phenomenon is similar to that of binary linear codes of dual distance at least
5, which was studied in previous work.
