When a quantum many-body system evolves under unitary dynamics that is punctuated by measurement, its dynamics can fall into one of two broad classes: (i) an “entangling” phase, in which the quantum entanglement between two subregions grows linearly in time and ultimately saturates at a value proportional to the subregion volume; and (ii) a “disentangling” phase, in which the entanglement growth rate vanishes and the final entanglement depends only on the area of the subregion boundary. In this talk I discuss our recent efforts to find an analytical solution for the properties of the phase transition separating these two phases. First, I consider the “infinite-dimensional” problem, in which all qubit pairs interact directly. In this case we can arrive at an exact solution for the transition, but only for a certain set of states that are post-selected based on the measurement outcome. I then discuss a version of the entanglement transition on tree-shaped tensor networks, for which we can solve exactly for the entanglement transition without postselection. Our results imply a straightforward experimental protocol for observing the transition experimentally without postselection.

Host: Tyler Ellison