Universal dynamics of monitored quantum and classical systems
Federico Gerbino
This thesis investigates the dynamics of information in monitored quantum and classical systems, focussing on its universal aspects. While in classical settings measurements do not affect the system’s evolution, in the quantum case they actively drive the dynamics. In particular, they suppress entanglement and, starting from a many-body mixed state, they lead to a pure state: this process is called purification. The first part of the thesis studies the purification dynamics of quantum many-body systems through effective random-matrix models. The rotational invariance in Hilbert space yields, in continuous time, a Dyson Brownian motion description, while in discrete time it leads to an algebraic formulation. We derive predictions for entanglement entropies in an appropriate scaling limit, revealing distinct universality classes associated with unitary and orthogonal invariance. We further analyse monitored Clifford circuits, belonging to a distinct universality class. The second part of the thesis develops classical analogues of monitored dynamics from a Bayesian perspective. We consider an observer tracking a random walker from noisy position measurements and updating the posterior occupation probability distribution using Bayes’ theorem. We use the Shannon entropy of the posterior distribution as our main observable. On the Cayley tree, the Shannon entropy undergoes a transition from a regime where it grows linearly in time to one where it remains bounded. In one dimension, the continuum limit description of the monitored dynamics allows the use of exact results from Kardar-Parisi-Zhang physics. We compute the behaviour of the Shannon entropy in various regimes. Together, these results clarify how the competition between measurements and information spreading gives rise to universal behaviour across quantum and classical settings.
Jury : John Chalker (rapporteur), Andrea De Luca (co-directeur de thèse), Satya Majumdar, Sara Murciano, Pedro Ribeiro, Grégory Schehr, Christophe Texier (directeur de thèse), Pierpaolo Vivo (rapporteur)