Ultrafast Entanglement Dynamics in Monitored Quantum Circuits

Projective measurement, a basic operation in quantum mechanics, can induce seemingly nonlocal effects. In this work, we analyze such effects in many-body systems by studying the nonequilibrium dynamics of weakly monitored quantum circuits, focusing on entanglement generation and information spreading. We find that, due to measurements, the entanglement dynamics in monitored circuits is indeed "faster" than that of unitary ones in several ways. Specifically, we find that a pair of well-separated regions can become entangled in a time scale e2/3, sublinear in their distance .e. For the case of Clifford monitored circuits, this originates from superballistically growing stabilizer generators of the evolving state. In addition, we find initially local information can spread superlinearly as t3/2. Furthermore, by viewing the dynamics as a dynamical encoding process, we show that the superlinear growing length scale relates to an encoding time that is sublinear in system size. To quantify the information dynamics, we develop a formalism generalizing operator spreading to nonunitary dynamics, which is of independent interest.