  We summarize recent developments at the interface of quantum gravity and
quantum information, and discuss applications to the quantum geometry of space
in loop quantum gravity. In particular, we describe the notions of link
entanglement, intertwiner entanglement, and boundary spin entanglement in a
spin-network state. We discuss how these notions encode the gluing of quanta of
space and their relevance for the reconstruction of a quantum geometry from a
network of entanglement structures. We then focus on the geometric entanglement
entropy of spin-network states at fixed spins, treated as a many-body system of
quantum polyhedra, and discuss the hierarchy of volume-law, area-law and
zero-law states. Using information theoretic bounds on the uncertainty of
geometric observables and on their correlations, we identify area-law states as
the corner of the Hilbert space that encodes a semiclassical geometry, and the
geometric entanglement entropy as a probe of semiclassicality.
