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When measured, a quantum system is subject to an unavoidable back-action, which makes the system evolve along stochastic quantum trajectories. Combined with unitary dynamics, this can lead to localization effects, like the quantum Zeno effect, and to the stabilization of new out-of-equilibrium steady-state in many-body systems. The recent characterization of these phases has shown that the universal properties of their phase transitions differ between individual quantum trajectories and their statistical ensemble. In this talk, I will review the description of quantum measurements and their back action in their discrete and continuous framework. I will first revisit the Zeno effect along individual (post-selected) trajectories and their statistical ensemble in an exactly solved single-qubit model. I will then extend the considerations to many-body systems and their measurement-induced phase transitions (MiPTs) and introduce a theory of partial post-selection, in which we restrict the stochastic dynamics to a controllable subset of quantum trajectories. Focusing on a Gaussian Majorana fermions model, I will show that the MiPT universality of the post-selected (single-trajectory) dynamics is stable against the inclusion of stochasticity from a small subset of quantum trajectories, but the monitored limit belongs to a different universality class. Our results provide a systematic way to study trajectory-averaged measurement-induced effects.

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Alessandro Romito, Lancaster University
Seminar Room 0.03, ETP
Contact: Michael Buchhold