The growth of entanglement in a quantum system changes qualitatively when it is observed more frequently than a certain critical rate, an important insight for describing quantum systems computationally.
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.
This is a conference proceeding in the framework of workshop "OpenQMBP2023" at Institute Pascal (Orsay, France) and associated to 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 results, 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 examining the field theory of critical ground states in Tomonaga-Luttinger liquids.
Dynamical phase transitions induced by local projective measurements have attracted a lot of attention in the past few years. It has been in particular argued that measurements may induce an abrupt change in the scaling law of the bipartite entanglement entropy. In this work we show that local projective measurements on a one-dimensional quadratic fermionic system induce a qualitative modification of the time growth of the entanglement entropy, changing from linear to logarithmic. However, in the stationary regime, the logarithmic behavior of the entanglement entropy does not survive in the thermodynamic limit and, for any finite value of the measurement rate, we numerically show the existence of a single area-law phase for the entanglement entropy. We give analytical arguments supporting our conclusions.