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Quantum work statistics, Loschmidt echo and information scrambling
A Chenu1,2, I L Egusquiza3, J Molina-Vilaplana4
1Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA. achenu@mit.edu.
Scientific Reports
|August 24, 2018
Summary
We establish a universal relation connecting quantum work probability distributions and Loschmidt echo dynamics. This links information scrambling to quantum work statistics via time-reversal operations.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Information theory
Background:
- The study of quantum work probability distributions is crucial for understanding energy exchange in quantum systems.
- Loschmidt echo dynamics probe the sensitivity of quantum systems to perturbations and time-reversal.
- Information scrambling quantifies how quantum information spreads within a system.
Purpose of the Study:
- To establish a universal relationship between quantum work statistics and Loschmidt echo dynamics.
- To demonstrate how Loschmidt echo of a specific state can measure information scrambling.
- To connect information scrambling to the analytic continuation of the partition function.
Main Methods:
- Derivation of a universal relation between quantum work probability distribution and Loschmidt echo.
- Analysis of the Loschmidt echo for a purified double thermofield state with a canonical initial density matrix.
- Investigation of quantum work statistics under a time-reversal operation (sudden Hamiltonian negation).
Main Results:
- A direct link is found between the quantum work probability distribution of isolated driven systems and Loschmidt echo dynamics.
- The Loschmidt echo of the purified double thermofield state serves as a direct measure of information scrambling.
- Information scrambling is quantitatively described by quantum work statistics under time-reversal.
Conclusions:
- The established relation provides a new perspective on quantum work and information scrambling.
- Loschmidt echo dynamics offer a powerful tool to probe information scrambling in quantum systems.
- The findings connect concepts from quantum thermodynamics, quantum information, and statistical mechanics.
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