We raise the question whether there is a way to characterize the quantum
information transport properties of a medium or material. For this analysis the
special features of quantum information have to be taken into account. We find
that quantum communication over an isotropic medium, as opposed to classical
information transfer, requires the transmitter to direct the signal towards the
receiver. Furthermore, for large classes of media there is a threshold, in the
sense that `sufficiently much' of the signal has to be collected. Therefore,
the medium's capacity for quantum communication can be characterized in terms
of how the size of the transmitter and receiver has to scale with the
transmission distance to maintain quantum information transmission. To
demonstrate the applicability of this concept, an n-dimensional spin lattice is
considered, yielding a sufficient scaling of d^(n/3) with the distance d
