Theory of free fermions dynamics under partial post-selected monitoring

Understand

Monitored quantum systems undergo Measurement-induced Phase Transitions (MiPTs) stemming from the interplay between measurements and unitary dynamics.

• When the detector readout is post-selected to match a given value, the dynamics is generated by a Non-Hermitian Hamiltonian with MiPTs characterized by different universal features.
• Here, we derive a partial post-selected stochastic Schr\"odinger equation based on a microscopic description of continuous weak measurement.
• This formalism connects the monitored and post-selected dynamics to a broader family of stochastic evolution.