Quantum trajectories and Page-curve entanglement dynamics

Abstract

We consider time dynamics of entanglement entropy (EE) between a filled fermionic system and an empty reservoir. We employ two different kinds of quantum trajectory approaches, namely stochastic unitary process and quantum state diffusion that mimics space-time white noise and quantum measurement at each local site of the lattice, respectively. For both protocols, we observe and characterize the full page curve-like dynamics for the EE. Depending on the protocol and the setup, we observe very distinct characteristics of the page curve and the associated Page time and page value. We also compute the number of fermions leaking to the reservoir and the associated current and shed light on their plausible connections with EE. Our approach is versatile, extendable to other setups and trajectory protocols, and potentially implementable in a variety of engineered quantum platforms.