# Fabio M. Mele

## Publications Authored By Fabio M. Mele

Motivated by the idea that, in the background-independent framework of a Quantum Theory of Gravity, entanglement is expected to play a key role in the reconstruction of spacetime geometry, we investigate the possibility of using the formalism of Geometric Quantum Mechanics (GQM) to give a tensorial characterization of entanglement on spin network states. Our analysis focuses on the simple case of a single link graph (Wilson line state) for which we define a dictionary to construct a Riemannian metric tensor and a symplectic structure on the space of states. The manifold of (pure) quantum states is then stratified in terms of orbits of equally entangled states and the block-coefficient matrices of the corresponding pulled-back tensors fully encode the information about separability and entanglement. Read More

We introduce the geometric formulation of Quantum Mechanics in the quantum gravity context, and we use it to give a tensorial characterization of entanglement on spin network states. Starting from the simplest case of a single-link graph (Wilson line), we define a dictionary to construct a Riemannian metric tensor and a symplectic structure on the space of spin network states, showing how they fully encode the information about separability and entanglement, and, in particular, an entanglement monotone interpreted as a distance with respect to the separable state. In the maximally entangled gauge-invariant case, the entanglement monotone is proportional to a power of the area of the surface dual to the link thus supporting a connection between entanglement and the (simplicial) geometric properties of spin network states. Read More