This lecture is part of the "Quantum Trajectories" program organized by the International Centre for Theoretical Sciences, featuring a talk by Aurelia Chenu on February 4, 2025 (Day 12, session 3). Explore cutting-edge research in quantum physics as part of a comprehensive program running from January 20 to February 7, 2025, at the Ramanujan Lecture Hall in ICTS Bengaluru. The program focuses on three main areas: quantum trajectories and control, measurement-induced phase transitions, and quantum information and computation. Join researchers from theoretical, experimental, and mathematical backgrounds as they present current research and foster collaborations in the field of quantum matter, contributing to the "second quantum revolution" that bridges quantum mechanics theory with practical applications in encryption, communication, and computing.