Multipartite Entanglement Structure of Monitored Quantum Circuits

Monitored quantum circuits have attracted significant interest as an example of synthetic quantum matter, intrinsically defined by their quantum information content. Here, we propose a multipartite entanglement perspective on monitored phases through the lens of quantum Fisher information. Our findings reveal that unstructured monitored random circuits fail to exhibit divergent multipartite entanglement even at criticality, highlighting their departure from standard quantum critical behavior. However, we demonstrate that genuinely multipartite entangled phases can be realized through two-site measurements, provided a protection mechanism is in place. This work positions multipartite entanglement as a valuable perspective for the study of interacting monitored circuits and broader frameworks of noisy quantum dynamics.