The measurement-induced phase transition

In a closed many-body quantum system, the entanglement between individual degrees of freedom generally increases over time. This entanglement growth can be seen as a quantum analog of the second law of thermodynamics. On the other hand, probing the state of one of these degrees of freedom causes the wavefunction to collapse to a given outcome, thus disentangling it from the system. Thus, there is a competition between entanglement production due to internal dynamics and its reduction by measurement in monitored quantum systems, which leads to a phase transition in the thermodynamic limit, dubbed "The Measurement-induced Phase Transition." 

In this talk, I’ll begin by explaining how this transition can be interpreted as a classical percolation transition, which captures the universal behavior of the phase transition in certain limits. I'll then discuss our ongoing efforts to explore the nature of the transition beyond these limits, including small-system numerical studies, analyses using tree tensor networks, and large-scale numerical simulations with Clifford circuits.