Random Matrix Theory Approach to Quantum Fisher Information in Quantum
Many-Body Systems
- URL: http://arxiv.org/abs/2402.09029v1
- Date: Wed, 14 Feb 2024 09:07:25 GMT
- Title: Random Matrix Theory Approach to Quantum Fisher Information in Quantum
Many-Body Systems
- Authors: Venelin P. Pavlov, Yoana R. Chorbadzhiyska, Charlie Nation, Diego
Porras, and Peter A. Ivanov
- Abstract summary: We theoretically investigate parameter quantum estimation in quantum chaotic systems.
Our analysis is based on an effective description of non-integrable quantum systems in terms of a random matrix Hamiltonian.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We theoretically investigate parameter quantum estimation in quantum chaotic
systems. Our analysis is based on an effective description of non-integrable
quantum systems in terms of a random matrix Hamiltonian. Based on this approach
we derive an analytical expression for the time evolution of the quantum Fisher
information. We test our random matrix theory prediction with the exact
diagonalization of a non-integrable spin system, focusing on the estimation of
a local magnetic field by measurements of the many-body state. Our numerical
calculations agree with the effective random matrix theory approach and show
that the information on the local Hamiltonian parameter is distributed
throughout the quantum system during the quantum thermalization process. Our
analysis shows a first stage in which the initial information spread is
quadratic in time which quickly passes into linear increase with slope
determine by the decay rate of the measured spin observable. When the
information is fully spread among all degrees of freedom a second quadratic
time scale determines the long time behaviour of the quantum Fisher
information.
Related papers
- Simulating NMR Spectra with a Quantum Computer [49.1574468325115]
This paper provides a formalization of the complete procedure of the simulation of a spin system's NMR spectrum.
We also explain how to diagonalize the Hamiltonian matrix with a quantum computer, thus enhancing the overall process's performance.
arXiv Detail & Related papers (2024-10-28T08:43:40Z) - Quantum information scrambling in adiabatically-driven critical systems [49.1574468325115]
Quantum information scrambling refers to the spread of the initially stored information over many degrees of freedom of a quantum many-body system.
We extend the notion of quantum information scrambling to critical quantum many-body systems undergoing an adiabatic evolution.
arXiv Detail & Related papers (2024-08-05T18:00:05Z) - A Theory of Quantum Jumps [44.99833362998488]
We study fluorescence and the phenomenon of quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field.
Our results amount to a derivation of the fundamental randomness in the quantum-mechanical description of microscopic systems.
arXiv Detail & Related papers (2024-04-16T11:00:46Z) - Continuously Monitored Quantum Systems beyond Lindblad Dynamics [68.8204255655161]
We study the probability distribution of the expectation value of a given observable over the possible quantum trajectories.
The measurements are applied to the entire system, having the effect of projecting the system into a product state.
arXiv Detail & Related papers (2023-05-06T18:09:17Z) - Universality of critical dynamics with finite entanglement [68.8204255655161]
We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement.
Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
arXiv Detail & Related papers (2023-01-23T19:23:54Z) - Probing cosmic string spacetime through parameter estimation [2.2945727928675734]
We estimate the deficit angle parameter by calculating its quantum Fisher information(QFI)
It is found that the quantum Fisher information depends on the deficit angle, evolution time, detector initial state, polarization direction, and its position.
Our results show that for different polarization cases the QFIs have different behaviors and different orders of magnitude, which may shed light on the exploration of cosmic string spacetime.
arXiv Detail & Related papers (2022-08-10T13:55:09Z) - Multiparameter Quantum Estimation Theory in Quantum Gaussian states [0.0]
This work concerns the computation of the analytical expression of the quantum Fisher information matrix (QFIM)
We give the analytical formulas of right logarithmic derivative (RLD) and symmetric logarithmic derivative (SLD) operators.
We also derive an explicit expression of the condition which ensures the saturation of the quantum Cram'er-Rao bound in estimating several parameters.
arXiv Detail & Related papers (2020-09-02T00:46:37Z) - Taking snapshots of a quantum thermalization process: emergent
classicality in quantum jump trajectories [0.0]
We show via a random matrix theory approach to nonintegrable quantum systems that the set of outcomes of the measurement of a macroscopic observable evolve in time like variables.
Our results show how to extend the framework of eigenstate thermalization to the prediction of properties of quantum measurements on an otherwise closed quantum system.
arXiv Detail & Related papers (2020-03-18T18:32:47Z) - Cosmology from Quantum Information [0.0]
We compute the corresponding quantum Fisher information function as the second derivative of the relative entanglement entropy for the density matrix at two different times.
We evaluate the minimal variance of quantum fluctuations that reproduces the power spectrum and the corresponding tilt in the slow roll limit.
arXiv Detail & Related papers (2020-02-11T10:36:38Z) - In and out of equilibrium quantum metrology with mean-field quantum
criticality [68.8204255655161]
We study the influence that collective transition phenomena have on quantum metrological protocols.
The single spherical quantum spin (SQS) serves as stereotypical toy model that allows analytical insights on a mean-field level.
arXiv Detail & Related papers (2020-01-09T19:20:42Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.