PIRSA:25060012 Conference Quantum Gravity

DOI10.48660/25060012

Conference/School: QIQG 2025

Vardhan, S. (2025). The free mutual information as a measure of quantum chaos. Perimeter Institute. https://pirsa.org/25060012

Vardhan, Shreya. The free mutual information as a measure of quantum chaos. Perimeter Institute, Jun. 24, 2025, https://pirsa.org/25060012 

@misc{ pirsa_PIRSA:25060012,
  doi = {10.48660/25060012},
  url = {https://pirsa.org/25060012},
  author = {Vardhan, Shreya},
  keywords = {Quantum Gravity, Quantum Information},
  language = {en},
  title = {The free mutual information as a measure of quantum chaos},
  publisher = {Perimeter Institute},
  year = {2025},
  month = {jun},
  note = {PIRSA:25060012 see, \url{https://pirsa.org}}
}

Abstract

I will introduce a quantity from noncommutative probability theory called the free mutual information, and discuss how it can be used as a new diagnostic of quantum many-body chaos. This quantity captures a notion of the spreading of the operator in the abstract space of all possible time-evolved operators, rather than the more familiar notion of spreading in the physical space of degrees of freedom. I will discuss a precise relation between the free mutual information and the higher-point out-of-time-ordered correlators which applies in any system. I will further discuss the behaviour of the free mutual information in a few representative models of chaotic systems, and how it is sensitive to features of the dynamics beyond those captured by the four-point out-of-time-ordered correlator.

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