  We give a complete characterization of pretty good state transfer on paths
between any pair of vertices with respect to the quantum walk model determined
by the XY-Hamiltonian. If $n$ is the length of the path, and the vertices are
indexed by the positive integers from 1 to $n$, with adjacent vertices having
consecutive indices, then the necessary and sufficient conditions for pretty
good state transfer between vertices $a$ and $b$ are that (a) $a + b = n + 1$,
(b) $n + 1$ has at most one odd non-trivial divisor, and (c) if $n = 2^t r -
1$, for $r$ odd and $r \neq 1$, then $a$ is a multiple of $2^{t - 1}$.
