Measurement and entanglement phase transitions in all-to-all quantum circuits

Quantum many-body systems subjected to local measurements at a nonzero rate can be in distinct dynamical phases, with differing entanglement properties. We introduce theoretical approaches to measurement-induced phase transitions in "all-to-all" quantum circuits with unitaries and measurements, in which any qubit can couple to any other. We first solve the simplest "minimal cut" toy model for entanglement dynamics in all-to-all circuits. We then show that certain all-to-all measurement circuits allow exact results by exploiting the circuit's local tree-like structure, and we compare these results with numerics in all-to-all circuits. We characterize the two different phases in all-to-all circuits using observables that are sensitive to the amount of information propagated between the initial and final time.