Long-range multipartite entanglement near measurement-induced transitions

Measurements profoundly impact quantum systems and can be used to create novel states of matter out of equilibrium. We investigate the multipartite entanglement structure that emerges in hybrid quantum circuits involving unitaries and measurements. We describe how a balance between measurements and unitary evolution can lead to multipartite entanglement spreading to distances far greater than what is found in nonmonitored systems, thus evading the usual fate of entanglement. We introduce a graphical representation based on spanning graphs that allows to infer the evolution of genuine multipartite entanglement for general subregions. We exemplify our findings on hybrid random Haar circuits that realize a 1D measurement-induced dynamical phase transition, where we find genuine three-party entanglement at all separations. At criticality, our data are consistent with power-law decay with a tripartite exponent strictly larger than the one of the bipartite logarithmic negativity. The four-party case is also explored. Finally, we discuss how our approach can provide fundamental insights regarding entanglement dynamics for a wide class of quantum circuits and architectures.