Chaos in quantum channels (1511.04021v3)

Abstract: We study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back up our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. These results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.

• The paper introduces a novel framework using OTOCs to quantify chaos in quantum channels.
• The study finds that OTOC decay leads to reduced mutual information and reveals scrambling via negative tripartite information.
• Empirical models including perfect tensor networks support that chaotic dynamics enhance fault-tolerance in quantum systems.

Overview of "Chaos in Quantum Channels"

The paper "Chaos in Quantum Channels" by Pavan Hosur, Xiao-Liang Qi, Daniel A. Roberts, and Beni Yoshida investigates the relationship between chaos and scrambling in quantum mechanical systems, particularly focusing on quantum channels—the mathematical constructs representing how quantum states evolve or transmit through a medium. The authors utilize unitary channels and analyze them through the lens of quantum information theory in order to paper the manifestation of chaos.

Key Contributions

1. Characterization Using Out-of-Time-Order Correlators (OTOCs): The authors utilize OTOCs to quantify chaos in unitary channels. These correlators are pivotal in diagnosing quantum chaos as they represent the degree of non-commutativity between operators at different times, indicative of the butterfly effect—a haLLMark of chaotic dynamics.
2. Mutual Information and Scrambling: The paper highlights that the decay of OTOCs implies that the mutual information between input and output subsystems in a quantum channel becomes negligible. Thus, scrambling—a process where information becomes widely dispersed across a system—is associated with the decay of OTOCs.
3. Tripartite Information as a Measure of Scrambling: The negativity of tripartite information among subsystems is proposed as a robust scrambling diagnostic. This measure suggests how information about the input becomes nonlocally spread across the output, making it inaccessible to local measurements.
4. Empirical Support Through Models: The theoretical findings are backed by numerical analysis in non-integrable and integrable models, as well as an analytic paper using perfect tensor networks—a model that captures chaotic time evolution. This multifaceted approach supports the hypothesis that chaos, characterized by the butterfly effect, necessitates the scrambling of information.

Implications and Speculation on Future AI Developments

• Quantum Information Processing:

This research provides deeper insights into quantum information processing capabilities, emphasizing the role of chaos in enhancing scrambling. In future technological advancements, it could be applied to improve quantum error correction and quantum computing efficiency, where robust scrambling and delocalization of information are desirable.

• Enhancing Fault-Tolerance:

Understanding the relationship between chaos and scrambling could lead to designing more fault-tolerant quantum systems. By leveraging unitary dynamics that maximize scrambling, quantum systems could be made inherently more resilient to information loss and local perturbations.

• Quantum Chaos Studies:

These findings contribute to the broader field of quantum chaos, offering a quantifiable framework to explore chaotic signatures in quantum channels. This offers potential applications in analyzing the thermalization and ergodicity of quantum systems.

The paper establishes a strong link between theoretical quantum information measures and physical phenomena associated with chaos, suggesting that future research could hinge on utilizing these insights to develop more advanced quantum technologies. By bridging chaos and quantum information theory, this work sets the stage for future explorations into the complexity and computational potential of quantum systems.