Measurement-induced entanglement transitions in quantum systems

P. K. Aravind

Han-Ze Li, Jianxin Zhong, Xue-Jia Yu

Measurement-induced entanglement phase transitions (MIETs) highlight how local measurements drive quantum systems between area-law and volume-law entangled states. This review surveys MIET in free fermion models, focusing on how unitary hopping competes with measurement-induced non-unitarity. We discuss controversies regarding the existence of MIET in one dimension, the impact of non-Hermitian skin effects, and potential experimental platforms. We conclude with open challenges, including feedback control and higher-dimensional extensions.

Dongheng Qian, Jing Wang

Measurement-induced entanglement (MIE) captures how local measurements generate long-range quantum correlations and drive dynamical phase transitions in many-body systems. Yet estimating MIE experimentally remains challenging: direct evaluation requires extensive post-selection over measurement outcomes, raising the question of whether MIE is accessible with only polynomial resources. We address this challenge by reframing MIE detection as a data-driven learning problem that assumes no prior knowledge of state preparation. Using measurement records alone, we train a neural network in a self-supervised manner to predict the uncertainty metric for MIE--the gap between upper and lower bounds of the average post-measurement bipartite entanglement. Applied to random circuits with one-dimensional all-to-all connectivity, our method reveals a learnability transition with increasing circuit depth: below a threshold the MIE can be effectively learned with resources that grow only polynomially with system size, whereas above it the required resources grow exponentially. This computational phase transition coincides with the breakdown of efficient classical simulation of the underlying quantum state. We further observe signatures of this transition on current noisy quantum devices. These results highlight the power of data-driven approaches for learning MIE and delineate the practical limits of its classical learnability.

Marco Piani, Gerardo Adesso

Gerardo Adesso, Marco Piani

Yu-Peng Wang, Chen Fang, Jie Ren

A quantum many-body system subject to unitary evolution and repeated local measurements with an increasing rate undergoes a measurement-induced entanglement transition from extensive (or subextensive) to area law entropy scaling. We find that certain open boundary systems under ``generalized monitoring,'' consisting of ``projective monitoring'' and conditional feedback, display an anomalous late-time particle concentration on the edge, reminiscent of the ``skin effect'' in non-Hermitian systems. Such feedback-induced skin effect will suppress the entanglement generation, rendering the system short-range entangled without measurement-induced entanglement transition. While initially emerged in noninteracting models, such skin effect can also occur in chaotic interacting systems and Floquet quantum circuits subjected to random generalized measurements. Since the dynamics of the skin effect do not require postselection and can be observed at the particle number level, the phenomenon is experimentally relevant and accessible in noisy intermediate-scale quantum platforms, such as trapped ions.