Measurement-induced phase transitions on dynamical quantum trees

Monitored many-body systems fall broadly into two dynamical phases, ``entangling'' or ``disentangling'', separated by a transition as a function of the rate at which measurements are made on the system. Producing an analytical theory of this measurement-induced transition is an outstanding challenge. So far, however, there are no exact solutions for dynamics of qubits with ``real'' measurements, whose outcome probabilities are sampled according to the Born rule. Here we define dynamical processes for qubits, with real measurements, that have a tree-like spacetime interaction graph. It yields an exactly solvable measurement transition. We explore these processes analytically and numerically, exploiting the recursive structure of the tree. Our model exhibits a transition at a nontrivial value of the measurement strength and an exponential scaling of the entanglement near the transition. On the basis of our results we propose a protocol for realizing a measurement phase transition experimentally via an expansion process.