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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

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Operator Entanglement in Interacting Integrable Quantum Systems: The Case of the Rule 54 Chain.

V Alba¹, J Dubail², M Medenjak³

¹Institute for Theoretical Physics, Universiteit van Amsterdam, Science Park 904, Postbus 94485, 1098 XH Amsterdam, Netherlands.

Physical Review Letters

|July 27, 2019

Summary

Operator entanglement in quantum systems distinguishes chaotic from integrable dynamics. This study shows operator entanglement grows logarithmically in interacting integrable systems, unlike the linear growth in chaotic systems.

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Area of Science:

Quantum mechanics
Many-body physics
Quantum information theory

Background:

Local operators in quantum systems spread over time.
Operator entanglement (entanglement entropy in operator space) is a potential indicator of chaotic vs. integrable dynamics.
Chaotic systems exhibit linear growth in operator entanglement, while integrable systems are less understood.

Purpose of the Study:

To investigate the growth of operator entanglement in interacting integrable quantum systems.
To provide an analytical upper bound for operator entanglement in such systems.
To distinguish between chaotic and integrable dynamics using operator entanglement.

Main Methods:

Analytical upper bound calculation for operator entanglement.
Study of the "Rule 54" qubit chain, a representative interacting integrable system.
Mapping system dynamics to stable quasiparticle scattering.

Main Results:

Operator entanglement grows logarithmically in interacting integrable systems, specifically the Rule 54 qubit chain.
This contrasts with the linear growth observed in chaotic systems.
The logarithmic growth is attributed to the elastic scattering of stable quasiparticles.

Conclusions:

Operator entanglement provides a clear distinction between chaotic and integrable dynamics.
Logarithmic growth of operator entanglement is characteristic of interacting integrable systems.
The findings offer insights into the behavior of quantum information in integrable models.