Entanglement negativity transition with measurement and feedforward

Abstract

In monitored quantum systems, where the dynamics consist of both measurements and unitary time evolution, the state of the system conditioned on measurement outcomes, also known as a trajectory, can be highly entangled. However, this entanglement is often obscured when we look at the unconditional state averaged over measurement outcomes. In this work, we show that the entanglement in trajectories can be revived in the unconditional state using local operations and classical communications. We uncover a sharp transition in the entanglement negativity of the unconditional state as a function of the number of measurement and feedforward channels acting on the system. The unconditional dynamics can also be viewed as the evolution of the system interacting with an environment, and the entanglement transition can be interpreted as a classical-to-quantum transition of the environment. We use tools from random matrix theory together with numerical simulations to shed light on the mechanism of this transition. Finally, we discuss an experimental protocol for observing this transition in engineered quantum devices.