  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 local (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
Schr\"odinger equation, such that various tools developed in quantum many-body
physics can be applied. The framework enables us to investigate a variety of
random quantum dynamics beyond Haar random circuits and Brownian circuits. We
perform numerical simulations for these models and demonstrate the validity and
prediction power of the entanglement feature approach.
