Related Experiment Video
Updated: Jun 12, 2025
09:23
Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
14.5K
Random matrix theory approach to quantum Fisher information in quantum ergodic systems
Venelin P Pavlov1, Yoana R Chorbadzhiyska1, Charlie Nation2
1Center for Quantum Technologies, Department of Physics, <a href="https://ror.org/02jv3k292">St. Kliment Ohridski University of Sofia</a>, James Bourchier 5 Blvd., 1164 Sofia, Bulgaria.
Physical Review. E
|September 19, 2024
Summary
We explored quantum parameter estimation in chaotic systems using random matrix theory. Our findings reveal three distinct timescales governing information spread and extraction during quantum thermalization.
Area of Science:
- Quantum Information Science
- Quantum Many-Body Systems
- Statistical Physics
Background:
- Quantum chaotic systems exhibit complex dynamics.
- Quantum parameter estimation quantifies information obtainable from quantum states.
- Random matrix theory effectively describes quantum ergodic systems.
Purpose of the Study:
- To theoretically investigate quantum parameter estimation in quantum chaotic systems.
- To derive an analytical expression for the time evolution of quantum Fisher information (QFI).
- To understand the timescales of information spreading during quantum thermalization.
Main Methods:
- Utilizing an effective description of quantum ergodic systems via a random matrix Hamiltonian.
- Deriving an analytical expression for the time evolution of QFI.
- Performing exact diagonalization of a nonintegrable spin system for numerical validation.
Main Results:
- Identified three distinct timescales governing QFI evolution.
- Observed initial quadratic QFI increase, followed by linear increase, and a final quadratic long-time behavior.
- Numerical results from a nonintegrable spin system validated the random matrix theory predictions.
Conclusions:
- The study provides an analytical framework for quantum parameter estimation in chaotic systems.
- Information on local Hamiltonian parameters distributes throughout the system during quantum thermalization.
- The findings offer insights into the dynamics of information in complex quantum systems.
Related Concept Videos
02:45The Quantum-Mechanical Model of an Atom
42.1K
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
42.1K
02:32The de Broglie Wavelength
25.4K
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
25.4K
04:08The Uncertainty Principle
23.2K
Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
23.2K
03:06The Pauli Exclusion Principle
35.5K
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
35.5K
01:08Fisher's Exact Test
393
Fisher's exact test is a statistical significance test widely used to analyze 2x2 contingency tables, particularly in situations where sample sizes are small. Unlike the chi-squared test, which approximates P-values and assumes minimum expected frequencies of at least five in each cell, Fisher's exact test calculates the exact probability (P-value) of observing the data or more extreme results under the null hypothesis. This feature makes it especially valuable when the assumptions of...
393
01:25Poisson's And Laplace's Equation
2.6K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
2.6K