Quantum Chaos, Randomness and Universal Scaling of Entanglement in Various Krylov Spaces

• URL: http://arxiv.org/abs/2407.11822v1
• Date: Tue, 16 Jul 2024 15:11:20 GMT
• Title: Quantum Chaos, Randomness and Universal Scaling of Entanglement in Various Krylov Spaces
• Authors: Hai-Long Shi, Augusto Smerzi, Luca Pezzè,
• Abstract summary: We derive an analytical expression for the time-averaged quantum Fisher information (QFI) that applies to all quantum chaotic systems governed by Dyson's ensembles. Our approach integrates concepts of randomness, multipartite entanglement and quantum chaos.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Using a random matrix approach, combined with the ergodicity hypothesis, we derive an analytical expression for the time-averaged quantum Fisher information (QFI) that applies to all quantum chaotic systems governed by Dyson's ensembles. Our approach integrates concepts of randomness, multipartite entanglement and quantum chaos. Furthermore, the QFI proves to be highly dependent on the dimension of the Krylov space confining the chaotic dynamics: it ranges from $N^2/3$ for $N$ qubits in the permutation-symmetric subspace (e.g. for chaotic kicked top models with long-range interactions), to $N$ when the dynamics extend over the full Hilbert space with or without bit reversal symmetry or parity symmetry (e.g. in chaotic models with short-range Ising-like interactions). In the former case, the QFI reveals multipartite entanglement among $N/3$ qubits. Interestingly this result can be related to isotropic substructures in the Wigner distribution of chaotic states and demonstrates the efficacy of quantum chaos for Heisenberg-scaling quantum metrology. Finally, our general expression for the QFI agrees with that obtained for random states and, differently from out-of-time-order-correlators, it can also distinguish chaotic from integrable unstable spin dynamics.

Related papers

• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Measuring Spectral Form Factor in Many-Body Chaotic and Localized Phases of Quantum Processors [22.983795509221974]
  We experimentally measure the spectral form factor (SFF) to probe the presence or absence of chaos in quantum many-body systems. This work unveils a new way of extracting the universal signatures of many-body quantum chaos in quantum devices by probing the correlations in eigenenergies and eigenstates.
  arXiv  Detail & Related papers  (2024-03-25T16:59:00Z)
• Distorted stability pattern and chaotic features for quantized prey-predator-like dynamics [0.0]
  Non-equilibrium and instability features of prey-predator-like systems are investigated in the framework of the Weyl-Wigner quantum mechanics. From the non-Liouvillian pattern driven by the associated Wigner currents, hyperbolic equilibrium and stability parameters are shown to be affected by quantum distortions.
  arXiv  Detail & Related papers  (2023-03-16T19:55:36Z)
• Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
  We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
  arXiv  Detail & Related papers  (2023-02-03T19:17:37Z)
• Geometric relative entropies and barycentric Rényi divergences [16.385815610837167]
  monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure. We show that monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure.
  arXiv  Detail & Related papers  (2022-07-28T17:58:59Z)
• Non-commutative phase-space Lotka-Volterra dynamics: the quantum analogue [0.0]
  The Lotka-Volterra (LV) dynamics is investigated in the framework of the Weyl-Wigner (WW) quantum mechanics (QM) The WW framework provides the ground for identifying how classical and quantum evolution coexist at different scales. The generality of the framework developed here extends the boundaries of the understanding of quantum-like effects on competitive microscopical bio-systems.
  arXiv  Detail & Related papers  (2022-06-14T11:23:04Z)
• Quantum dynamics corresponding to chaotic BKL scenario [62.997667081978825]
  Quantization smears the gravitational singularity avoiding its localization in the configuration space. Results suggest that the generic singularity of general relativity can be avoided at quantum level.
  arXiv  Detail & Related papers  (2022-04-24T13:32:45Z)
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect [68.8204255655161]
  We show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.
  arXiv  Detail & Related papers  (2021-12-08T11:41:38Z)
• Probing quantum chaos in multipartite systems [4.771483851099131]
  We show that the contribution of the subsystems to the global behavior can be revealed by probing the full counting statistics. We show that signatures of quantum chaos in the time domain dictate a dip-ramp-plateau structure in the characteristic function. Global quantum chaos can be suppressed at strong coupling.
  arXiv  Detail & Related papers  (2021-11-24T13:06:25Z)
• Many-Body Quantum Chaos and Space-time Translational Invariance [0.0]
  We study the consequences of having translational invariance in space and in time in many-body quantum chaotic systems. We consider an ensemble of random quantum circuits, composed of single-site random unitaries and nearest neighbour couplings. We numerically demonstrate, with simulations of two distinct circuit models, that in such a scaling limit, most microscopic details become unimportant.
  arXiv  Detail & Related papers  (2021-09-09T18:00:00Z)
• Dynamic Kibble-Zurek scaling framework for open dissipative many-body systems crossing quantum transitions [0.0]
  We study the quantum dynamics of many-body systems, in the presence of dissipation, under Kibble-Zurek protocols. We focus on a class of dissipative mechanisms whose dynamics can be reliably described through a Lindblad master equation.
  arXiv  Detail & Related papers  (2020-03-17T10:01:39Z)

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.