Measurement-Induced Phase Transitions: From Ensembles of Quantum Trajectories to Most-Likely Dynamics
Quantum systems exhibit complex dynamics characterised by information scrambling, giving rise to phenomena such as long-range entanglement and thermalisation. Local measurements can profoundly alter these dynamics by freezing local degrees of freedom, leading to new stationary state distributions and associated measurement-induced phase transitions (MiPTs). While measurement-induced dynamics is inherently stochastic, post-selecting specific detector readouts to isolate individual quantum trajectories yields deterministic dynamics with distinct phase transition characteristics.
In this talk, I contrast the quantum dynamics of individual post-selected trajectories with their collective statistical behaviour. I introduce a novel partially post-selected stochastic Schrödinger equation that captures controllable subsets of quantum trajectories, and exploit it to define the concept of the most likely trajectory. I demonstrate this framework on paradigmatic systems of Gaussian fermions and bosons, showing that the most-likely dynamics reproduces key qualitative features of the full ensemble dynamics. I further apply the formalism to interacting bosons in the Sine-Gordon model, where the most-likely trajectory approach captures the dynamics through a self-consistent harmonic approximation and reveals an entanglement phase transition from area-law to logarithmic-law scaling.
Together, these results establish a powerful framework for studying MiPTs in monitored quantum systems via deterministic nonlinear equations, applicable to both fermionic and bosonic platforms.
Based on
[1] Chun Y. Leung, Dganit Meidan and Alessandro Romito, Phys. Rev. X 15, 021020 (2025)
[2] Anna Delmonte, Zejian Li, Rosario Fazio and Alessandro Romito, SciPost Phys. 20, 109 (2026)