Observing measurement-induced entanglement transitions using a mixed-state entanglement measure

Measurement in Quantum Mechanics is among the most fundamental and debated processes in modern physics. In theory, it can be described by pure stochastic quantum trajectories, or continuous master equations for the mixed state. Whereas both descriptions lead to the same measurement statistics for linear observables, the quantum trajectory entanglement shows measurement-induced transitions (MITs) invisible to the steady-state density matrix. Moreover, there is no standard way to quantify the entanglement of mixed states. Recently, we have introduced the "configuration coherence", a mixed-state entanglement measure for systems with a fixed conserved charge. Here, we employ the configuration coherence to demonstrate that entanglement in both the trajectories and master equation approaches reveal the MIT. Our finding suggests that the MIT is a manifestation of coherent-to-diffusive crossover in quantum random walks.