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A Knowledge Graph Approach to Elucidate the Role of Organellar Pathways in Disease via Biomedical Reports

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Fast scrambling on sparse graphs.

Gregory Bentsen¹, Yingfei Gu², Andrew Lucas³

¹Department of Physics, Stanford University, Stanford, CA 94305.

Proceedings of the National Academy of Sciences of the United States of America

|March 23, 2019

Summary

This summary is machine-generated.

Quantum information scrambles logarithmically with system size in generic quantum systems at infinite temperature. This finding bounds scrambling time by local correlation decay, offering insights into quantum chaos and black hole analogies.

Keywords:

quantum chaos quantum entanglement quantum information random graphs

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Area of Science:

Quantum Physics
Many-Body Systems
Quantum Information Theory

Background:

Understanding how quantum information spreads and becomes inaccessible (scrambling) is crucial for quantum many-body systems.
The fast-scrambling conjecture posits that scrambling time scales at least logarithmically with the number of degrees of freedom (N).

Purpose of the Study:

To derive a bound on the scrambling time for generic quantum systems at infinite temperature.
To investigate the relationship between quantum chaos and information scrambling.
To explore experimental methods for studying scrambling in quantum systems.

Main Methods:

Derivation of a scrambling time inequality for generic quantum systems.
Utilizing Lieb-Robinson bounds and generalized Sachdev-Ye-Kitaev (SYK) models.
Analysis of random unitary circuits and their properties.

Main Results:

A logarithmic bound on scrambling time is derived for generic quantum systems at infinite temperature.
Scrambling time is shown to be limited by the decay time of local quantum correlations.
Demonstration that logarithmic scrambling time can be achieved in systems with sparse connectivity.
Construction of models exhibiting quantum chaos (infinite Lyapunov exponent) but logarithmic scrambling time.

Conclusions:

Quantum information scrambling in generic systems at infinite temperature is bounded logarithmically.
Quantum chaos and scrambling are not universally linked; systems can be chaotic without fast scrambling.
The study provides a theoretical framework and experimental suggestions for probing quantum scrambling.