Quantum trajectories and Page-curve entanglement dynamics

TL;DR

This paper investigates the time evolution of entanglement entropy in fermionic systems interacting with reservoirs, using quantum trajectory methods to reveal Page curve-like dynamics and their dependence on different dephasing scenarios.

Contribution

It introduces a detailed analysis of entanglement dynamics using stochastic quantum trajectories, highlighting distinct Page curve behaviors under various dephasing protocols.

Findings

Full Page curve-like entanglement dynamics observed

Distinct Page times and values depending on protocols

Connections between fermion leakage, current, and entanglement

Abstract

We consider time dynamics of entanglement entropy between a filled fermionic system and an empty reservoir. We consider scenarios (i) where the system is subjected to a dephasing mechanism and the reservoir is clean, thereby emulating expansion of effectively interacting fermions in vacuum, and (ii) where both the system and the reservoir are subjected to dephasing and thereby enabling us to address how the entanglement between the part of the effectively interacting system and its complement evolves in time. We consider two different kinds of quantum trajectory approaches, namely stochastic unitary unraveling and quantum state diffusion. For both protocols, we observe and characterize the full Page curve-like dynamics for the entanglement entropy. 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 entanglement entropy. Our findings are expected to hold for a wide variety of generic interacting quantum systems.