Exponential Shortcut to Measurement-Induced Entanglement Phase Transitions

Recently discovered measurement-induced entanglement phase transitions in monitored quantum circuits provide a novel example of far-from-equilibrium criticality. Here, we propose highly efficient strategy for experimentally accessing these through fluctuations. Instead directly measuring entropy, which requires an exponential number measurements the subsystem size, our method provides scalable approach to presence conserved quantities. In analogy entropy and mutual information, illustrate how bipartite multipartite fluctuations can both be employed analyze Remarkably, transition revealed by only handful qubits.