Dynamical entanglement percolation with spatially correlated disorder

The distribution of entanglement between the nodes of a quantum network plays a fundamental role in quantum information applications. In this work, we investigate the dynamics of a network of qubits where each edge corresponds to an independent two-qubit interaction. By applying tools from percolation theory, we study how entanglement dynamically spreads across the network. We show that the interplay between unitary evolution and spatially correlated disorder leads to a non-standard percolation phenomenology, significantly richer than uniform bond percolation and featuring hysteresis. A two-colour correlated bond percolation model, whose phase diagram is determined via numerical simulations and a mean-field theory, fully elucidates the physics behind this phenomenon.