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Area of Science:

  • Quantum Information Theory
  • Statistical Mechanics
  • Quantum Chaos

Background:

  • Information scrambling in quantum systems is quantified by out-of-time-ordered correlators.
  • The Lyapunov exponent, measuring scrambling rate, is predicted to obey a universal bound.
  • Previous work suggested a quantum-statistical origin for this bound.

Purpose of the Study:

  • To elucidate the quantum-statistical origins of the universal bound on information scrambling.
  • To demonstrate the necessity of quantum thermal fluctuations for reproducing the bound.
  • To establish a link between instanton stability and the quantum chaos bound.

Main Methods:

  • Utilizing path-integral techniques to model quantum dynamics.
  • Incorporating quantum thermal fluctuations (tunneling, zero-point energy) into classical dynamics.
  • Propagating quantum-Boltzmann-conserving classical dynamics for a system with a potential barrier.

Main Results:

  • A minimal theory reproducing the bound requires contributions from quantum thermal fluctuations.
  • The bound is governed by the stability of thermal fluctuations around barrier instantons.
  • Instanton formation and stability are intrinsically linked to the quantum chaos bound.

Conclusions:

  • Quantum thermal fluctuations are essential for imposing the universal bound on quantum information scrambling.
  • The stability of instanton-dominated thermal fluctuations dictates the scrambling rate bound.
  • A fundamental connection exists between delocalized structures like instantons and the quantum chaos bound.