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