Cahier de l'Institut Pascal: Noisy Quantum Dynamics and Measurement-Induced Phase Transitions

TL;DR

This paper analyzes measurement-induced phase transitions in quantum systems, especially hybrid circuits, highlighting how measurement rates influence entanglement dynamics and phase behavior.

Contribution

It provides a comprehensive analysis of measurement-induced phase transitions in 1D quantum circuits, including entanglement regimes and non-local measurement effects.

Findings

Measurement rate induces phase transitions in entanglement properties.

Three entanglement regimes identified: area law, volume law, and logarithmic growth.

Non-local effects of local measurements studied via Tomonaga-Luttinger liquids.

Abstract

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.