Entanglement Growth from Entangled States: A Unified Perspective on Entanglement Generation and Transport

Studies of entanglement dynamics in quantum many-body systems have focused largely on initial product states. Here, we investigate the far richer dynamics from initial entangled states, uncovering universal patterns across diverse systems ranging from many-body localization (MBL) to random quantum circuits. Our central finding is that the growth of entanglement entropy can exhibit a counter-intuitive non-monotonic dependence on the initial entanglement in many non-ergodic systems, peaking for moderately entangled initial states. To understand this phenomenon, we introduce a conceptual framework that decomposes entanglement growth into two mechanisms: ``build'' and ``move''. The ``build'' mechanism creates new entanglement, while the ``move'' mechanism redistributes pre-existing entanglement throughout the system. Specifically, we demonstrate that MBL dynamics are ``move-dominated'', exhibiting a quantitative agreement with a random SWAP circuit that serves as a model of pure ``move'' dynamics by uniformly distributing pre-existing entanglement. This implies that MBL acts as a redistributor of a hidden entanglement reservoir quantified by the bipartition-averaged entropy. This ``build-move'' framework offers a unified perspective for classifying diverse physical dynamics, deepening our understanding of entanglement propagation and information processing in quantum many-body systems.