  In a one-dimensional Heisenberg chain, we show that there are no sets of
coupling strengths such that the evolution perfectly transfers a quantum state
between the two ends of the chain without the addition of magnetic fields. In
lieu of perfect transfer, we consider a range of options for achieving high
quality transfer, whether in finite time, or via "pretty good" transfer where
one waits long times in the hope of getting arbitrarily close to perfect
transfer. In attempting to engineer arbitrarily accurate transfer, we explore a
new paradigm that facilitates time estimates for achieving any target accuracy
$\epsilon$ for the transfer.
