- The paper introduces a framework combining stochastic Schrödinger evolution, generalized hydrodynamics, and a collapsed quasiparticle pair ansatz to predict entanglement dynamics.
- It demonstrates that even weak continuous measurements trigger a transition from volume law to area law entanglement in free fermion systems.
- Numerical simulations validate the model by efficiently tracking entanglement entropy through two-point correlation functions.
Entanglement in a Free Fermion Chain under Continuous Monitoring
The paper investigates the dynamics of entanglement entropy in a free fermion chain subject to continuous monitoring. The research is situated within the broader context of understanding entanglement in quantum systems, particularly how it interacts with measurement processes. The paper employs a model of free fermions on a one-dimensional lattice with a Hamiltonian that includes continuous monitoring of local occupation numbers.
Key Contributions and Methodological Framework
The central contribution is a proposed theory for the evolution of entanglement entropy starting from disentangled and highly excited initial states. It leverages generalized hydrodynamics (GHD) and the concept of quasi-particle pairs, which are instrumental in describing entanglement dynamics in integrable systems.
- Dynamic Framework:
- The system under paper follows a stochastic Schrödinger equation that describes how the quantum state evolves under the influence of both unitary Hamiltonian dynamics and measurement-induced dynamics.
- The authors derive a GHD equation that extends standard hydrodynamic descriptions to incorporate measurement effects. This results in a model where quasiparticle momenta are redistributed due to continuous monitoring.
- Collapsed Quasiparticle Pair Ansatz:
- The entanglement dynamics are conjectured to be described by the periodic collapse and recreation of quasiparticle pairs. Each pair is created randomly in momentum space, affecting the entanglement entropy.
- The approach predicts that weak continuous measurements destabilize the volume law entanglement, resulting instead in an area law entanglement in the stationary state.
- Numerical Simulations:
- Extensive numerical simulations validate the theoretical predictions, showing good agreement between simulations and the proposed ansatz.
- The simulations utilize Gaussianity preservation in the quantum trajectories to efficiently evaluate the entanglement entropy through two-point correlation functions.
Implications and Future Directions
The research highlights the delicate interplay between unitary dynamics and measurement in quantum systems. The findings suggest that continuous measurement plays a significant role in suppressing long-range entanglement, providing insights into how quantum information might be controlled or harnessed in practical scenarios involving open quantum systems.
Theoretical and Practical Implications:
- Non-Interacting Systems:
- For non-interacting (free) systems, the paper predicts entanglement suppression under even weak measurements. This challenges the intuitions developed for closed systems and underscores the transformative effect of measurement-induced decoherence.
- Generalization to Other Systems:
- While the focus is on non-interacting systems, the methodology and insights could extend to integrable systems with interactions or even chaotic systems, potentially revealing universal features of the entanglement-measurement interplay.
- Entanglement Structure:
- Despite the reduction in total entanglement, the presence of measurement can distill the entanglement among quasiparticles, suggesting pathways to optimize or utilize entanglement in quantum systems.
The results open avenues for further research into the role of measurement in more complex systems and quantum simulators, especially considering the impact on quantum thermodynamics and quantum information tasks. The approach also invites exploration into whether similar dynamics emerge under different quantum measurement schemes or with the inclusion of interactions in the model.