  In this work we seek to generalize the connection between traversable
wormholes and quantum channels. We do this via a connection between traversable
wormholes and graph geometries on which we can perform quantum random walks for
signal transmission. As a proof of principle, we give an example of a geometry
for which quantum random walk signal traversal occurs exponentially faster than
a standard ballistic classical traversal. We then generalize this connection to
superpositions over holographic states, and argue that the quantum random
walk/graph geometry picture works to study quantum channel properties of such
states.
