Measurement-induced criticality in random quantum circuits

A new class of quantum entanglement transitions separating phases with different entanglement entropy scaling has been observed in recent numerical studies. Despite the numerical efforts, an analytical understanding of such transitions has remained elusive. Here, the authors propose a theory for the area-law to volume-law entanglement transition in many-body systems that undergo both random unitary evolutions and projective measurements. Using the replica method, the authors map analytically this entanglement transition to an ordering transition in a classical statistical mechanics model. They derive the general entanglement scaling properties at the transition and show a solvable limit where this transition can be mapped onto two-dimensional percolation.