Structure of multipartite entanglement at measurement induced phase transitions

Monitored random quantum circuits, when taken to the measurement induced phase transition, tend to have a very rare property: genuine multipartite entanglement that is both long ranged (following power law decay over distance) and accessible on the level of small subregions. This property emerges from the balancing act between gates that entangle different qubits and measurements that help break up large entangled structures. In this talk, we will start with a heuristic model of this balance which will, in turn, imply important properties for the power-law decay exponents of multipartite entanglement in these systems. In particular, it demonstrates why these scaling exponents should be subadditive in the number of parties entangled, so that high-party entanglement cannot be abnormally suppressed. We then provide an analysis of these exponents in the measurement-only circuit describing a projective Ising model, where we can use the connection to the percolation model conformal field theory to prove that the scaling exponents are exactly twice the number of parties. Finally, we perform large-scale simulations in the universality class of Haar random unitaries at the measurement induced phase transition point. Here we find strictly subadditive exponents, and make a connection to our original heuristic model through the entanglement-weighted graph.