Cross Entropy Benchmark for Measurement-Induced Phase Transitions

Open quantum dynamics can host a rich phenomenology, including a family of measurement-induced phase transitions (MIPT) in the scaling of entanglement along quantum trajectories in monitored systems. While the MIPT occurs generically in a number of different models, its verification can be challenging even on an error-corrected quantum computer, due to the so-called ``postselection problem". I will describe the prospects of employing the linear cross-entropy to experimentally access measurement-induced phase transitions (MIPT) without requiring any postselection of quantum trajectories. By running two random circuits that are identical in the bulk but with different initial states - one on a quantum and the other on a classical computer - the linear cross entropy between the bulk measurement outcome distributions in the two circuits can be used to distinguish the volume law from area law phases. Besides the volume-law to area law MIPT, the linear cross-entropy can be employed to access other dynamical phase transitions in monitored systems, as I will describe.