Alessandro Santini — Scuola Internazionale Superiore di Studi Avanzati (SISSA) #
Quantum Trajectories and Probability Distributions: Uncovering the Dynamics of Monitored Quantum Many-body Systems #
We explore the non-equilibrium dynamics of many-body quantum systems under the influence of measurement protocols. Recent studies have shown that measurements can induce different non-equilibrium regimes, leading to abrupt changes in the scaling laws of bipartite entanglement entropy. Specifically, we investigate measurement-induced phase transitions in a monitored Quantum Ising chain [1]. Employing continuous local projective measurements, we witness the transition investigating the out-of-equilibrium probability distribution functions of local observables. Additionally, we extend our investigation by introducing an analytical framework designed to assess the probability distributions of expectation values across possible quantum trajectories [2]. We demonstrate this method through the analysis of two scenarios: a single qubit subjected to magnetization measurements and a free particle undergoing position measurements.  [1] Continuously monitored quantum systems beyond Lindblad dynamics, G. Lami, A. Santini, M. Collura, New J. Phys. 26 023041 (2024) [2] Full counting statistics as a probe of measurement-induced transitions in the quantum Ising chain, E. Tirrito, A. Santini, R. Fazio, M. Collura, SciPost Phys. 15, 096 (2023)