  We discuss the basic problem of signal transmission in quantum mechanics in
terms of topological theories. Using the analogy between knot diagrams and
quantum amplitudes we calculate the transmission coefficients of the concept
topological quantum devices that realize the knot topology. We observe that the
problem is in different ways similar to that of transmission on quantum graphs.
The desired transmission or filtering properties can be attained by the
variation of the topology of the device, or an external parameter, which in our
model controls the topological phase. One interesting property of the
transmission coefficients is the existence of "self-averaging" phases, in which
the value of the transmission coefficient is independent from all the
representatives in a chosen family of knots. We briefly discuss physical
realizations of the concept devices.
