Long Range Multipartite Entanglement Near Measurement-Induced Transitions

Projective measurements in random quantum circuits can generate different kinds of steady state entanglement properties of a quantum state. Such systems are said to undergo a measurement induced phase transition between two entanglement phases: an area law phase and volume law phase. In our work, we study the genuine 3-party entanglement properties of quantum states in both of the area and volume law regimes as well as near the measurement-induced phase transition in 1D Haar random circuits. We find genuine 3-party entanglement that can persist even at large separations which is in contrast to equilibrium behaviour of many systems. We explain these results by analyzing the geometric entanglement of a quantum state in the circuit layer by layer. Lastly, we introduce a graphical tool called minimal spanning graphs to help in visualizing how genuine multipartite entanglement can arise in these kinds of systems.