  Spin networks are endowed with an Information Transfer Fidelity (ITF), which
defines an absolute upper bound on the probability of transmission of an
excitation from one spin to another. The ITF is easily computable but the bound
can be reached asymptotically in time only under certain conditions. General
conditions for attainability of the bound are established and the process of
achiev-ing the maximum transfer probability is given a dynamical model, the
translation on the torus. The time to reach the maximum probability is
estimated using the simultaneous Diophantine approximation, implemented using a
variant of the Lenstra-Lenstra-Lovasz (LLL) algorithm. For a ring with uniform
couplings, the network can be made a metric space by defining a distance
(satisfying the triangle inequality) that quantifies the lack of transmission
fidelity between two nodes. It is shown that transfer fidelities and transfer
times can be improved significantly by means of simple controls taking the form
of non-dynamic, spatially localized bias fields, opening up the possibility for
intelligent design of spin networks and dynamic routing of information encoded
in them, while being more flexible than engineering fixed couplings to favor
some transfers, and less demanding than control schemes requiring fast dynamic
controls.
