This is a conference proceeding in the framework of workshop “OpenQMBP2023”* at Institute Pascal (Orsay, France) and associated with the lecture given by Prof. Ehud Altman. We provide a comprehensive analysis of recent results in the context of measurement-induced phase transitions (MIPT) in quantum systems, with a particular focus on hybrid quantum circuits as a model system in one-dimension. Recent resutls, demonstrate how varying the rate of projective measurements can induce phase transitions, resulting in abrupt changes in the properties of the entanglement. The interplay between unitary evolution and measurement processes can be investigated, through mappings to classical statistical models and the application of replica field theory techniques. Starting from a low-entangled state, there can be three regimes characterized by different dynamics of bipartite entanglement entropies for a portion of the system: high-rate measurements leading to rapid entanglement saturation (area law), low-rate measurements allowing linear entanglement growth (up to volume law), and a critical rate at which entanglement grows logarithmically. Finally, we present results on the non-local effects of local measurements by ex-amining the field theory of critical ground states in Tomonaga-Luttinger liquids.
Christopoulos et al. (Tue,) studied this question.