Markovian Entanglement Dynamics under Locally Scrambled Quantum Evolution

We study the time evolution of quantum entanglement for a specific class of quantum dynamics, namely the locally scrambled quantum dynamics, where each step of the unitary evolution is drawn from a random ensemble that is invariant under on-site basis transformations. In this case, the average entanglement entropy follows Markovian dynamics that the entanglement property of the future state can be predicted solely based on the entanglement properties of the current state and the unitary operator at each step. We introduce the entanglement feature formulation to concisely organize the entanglement entropies over all subsystems into a many-body wave function, which allows us to describe the entanglement dynamics using an imaginary-time Schrodinger equation, such that various tools developed in quantum many-body physics can be applied. In addition to Haar random circuits and Brownian circuits, we also study a new type of circuit — fractional swap circuit in which the two local qudits are partially exchanged and partially staying on the same site. We further investigate the bipartite operator mutual information and tripartite operator mutual information of the fractional swap circuit and compare with different CFT results.