  Recent work has shown that a simple chain of interacting spins can be used as
a medium for high-fidelity quantum communication. We describe a scheme for
quantum communication using a spin system that conserves z-spin, but otherwise
is arbitrary. The sender and receiver are assumed to directly control several
spins each, with the sender encoding the message state onto the larger
state-space of her control spins. We show how to find the encoding that
maximises the fidelity of communication, using a simple method based on the
singular-value decomposition. Also, we show that this solution can be used to
increase communication fidelity in a rather different circumstance: where no
encoding of initial states is used, but where the sender and receiver control
exactly two spins each and vary the interactions on those spins over time. The
methods presented are computationally efficient, and numerical examples are
given for systems having up to 300 spins.
