  We study the holographic properties of a class of quantum geometry states
characterized by a superposition of discrete geometric data, in the form of
generalised tensor networks. This class specifically includes spin networks,
the kinematic states of lattice gauge theory and discrete quantum gravity. We
employ an algebraic, operatorial definition of holography based on quantum
information channels, an approach which is particularly valuable in settings,
such as the one we consider, where the relevant Hilbert space of states does
not factorize into subsystem Hilbert spaces due to gauge invariance. We apply
random tensor network techniques (successfully used in the AdS/CFT context) to
analyse information transport properties of the bulk-to-boundary and
boundary-to-boundary maps associated with this superposition of quantum
geometries, and produce typicality results about the average over the geometric
data colouring the fixed graph structure. In this context, one naturally
obtains a nontrivial area operator encoding the dominant contribution to
entropy calculations. Among our main results is the requirement that one can
only isometrically map a bulk region onto boundaries with fixed total area. We
furthermore inquire about similar state-induced mappings between segments of
the boundary, and discuss related conditions for isometric behaviour. These
generalisations make further steps towards quantum gravity implementations of
tensor network holography.
