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Relative Entropy of Random States and Black Holes
1Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA.
Physical Review Letters
|May 14, 2021
Summary
We developed a new method to calculate the relative entropy of quantum states, finding that black hole microstates are distinguishable. This work advances understanding of quantum information and the AdS/CFT correspondence.
Area of Science:
- Quantum Information Theory
- Statistical Mechanics
- High Energy Physics
Background:
- Understanding quantum entanglement and information scrambling is crucial in quantum mechanics.
- The relative entropy quantifies the distinguishability between quantum states.
- Eigenstate thermalization hypothesis (SETH) describes thermalization in chaotic quantum systems.
Purpose of the Study:
- To develop an analytic technique for calculating the relative entropy of highly excited quantum states.
- To investigate the distinguishability of black hole microstates within the AdS/CFT correspondence.
- To test the subsystem eigenstate thermalization hypothesis (SETH) in holographic systems.
Main Methods:
- Sampling quantum states from the Wishart ensemble.
- Developing a large-N diagrammatic technique for relative entropy calculation.
- Comparing analytic results with numerical simulations for validation.
Main Results:
- An exact analytic solution for relative entropy expressed in elementary functions.
- Precise agreement between analytic predictions and small-N numerical data.
- Confirmation that random matrix theory accurately models chaotic many-body eigenstates, supporting eigenstate thermalization.
- Demonstration that black hole microstates are distinguishable even with limited observer access.
- Distinguishability of black hole microstates found to be nonperturbatively small in Newton's constant.
Conclusions:
- Holographic systems adhere to the subsystem eigenstate thermalization hypothesis (SETH) for subsystems up to half the total system size.
- The developed formalism provides a powerful tool for studying quantum information in quantum gravity.
- Relative entropy offers insights into the nature of quantum information and thermalization in complex quantum systems.
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