  A continuous quantum walk on a graph $X$ with adjacency matrix $A$ is
specified by the 1-parameter family of unitary matrices $U(t)=\exp(itA)$. These
matrices act on the state space of a quantum system, the states of which we may
represent by density matrices, positive semidefinite matrices with rows and
columns indexed by $V(X)$ and with trace $1$. The square of the absolute values
of the entries of a column of $U(t)$ define a probability density on $V(X)$,
and it is precisely these densities that predict the outcomes of measurements.
There are two special cases of physical interest: when the column density is
supported on a vertex, and when it is uniform. In the first case we have
perfect state transfer; in the second, uniform mixing.
  There are many results concerning state transfer and uniform mixing. In this
paper we show that these results on perfect state transfer hold largely because
at the time it occurs, the density matrix is real. We also show that the
results on uniform mixing obtained so far hold because the entries of the
density matrix are algebraic numbers. As a consequence of these we derive
strong restrictions on the occurence of uniform mixing on bipartite graphs and
on oriented graphs.
