Information geometry of non-equilibrium quantum states: Mixed metric structures on an extended information manifold

• URL: http://arxiv.org/abs/2609.00977v1
• Date: Tue, 01 Sep 2026 09:33:32 GMT
• Title: Information geometry of non-equilibrium quantum states: Mixed metric structures on an extended information manifold
• Abstract summary: We discuss an information-geometric framework for characterizing quantum states in non-equilibrium dynamics.<n>The framework treats $h$ and $t$ as coordinates of an extended information manifold $(h,t)$.<n>The geometric observables characterize the speed of evolution on the manifold and the alignment between the temporal and parameter-deformation directions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We discuss an information-geometric framework for characterizing quantum states in non-equilibrium dynamics. Using the transverse-field Ising chain model as a laboratory, we investigate the quantum Fisher information metric with particular emphasis on the mixed metric component $g_{ht}$ and related geometric observables, where $h$ is a controllable post-quench Hamiltonian parameter and $t$ is real time. The framework treats $h$ and $t$ as coordinates of an extended information manifold $(h,t)$. The geometric observables characterize the speed of evolution on the manifold and the alignment between the temporal and parameter-deformation directions. Correlations between these geometric quantities and two widely used measures of non-equilibrium dynamics, the entanglement entropy and the Loschmidt echo, are analyzed.

Related papers

• Geometry of Noisy Quantum Many-Body Dynamics with Continuous Symmetries: Entanglement and Correlations [0.0]
  We study unitary quantum dynamics in noisy Brownian models with global continuous symmetries.<n>This work focuses on Rényi entanglement entropies and hydrodynamic and non-hydrodynamic correlators.
  arXiv  Detail & Related papers  (2026-08-11T18:00:01Z)
• A Gauge-Covariant Geometric Framework for Non-Hermitian Quantum Systems [0.0]
  We develop a comprehensive, gauge-covariant geometric framework for non-Hermitian quantum systems.<n>We show that the non-Hermitian geometric curvature originates from the non-commutativity of the stretching components at the operator level.<n>We also examine physical realizations of this model, including the non-Hermitian Su--Schrieffer--Heeger (SSH) and Hatano--Nelson (HN)
  arXiv  Detail & Related papers  (2026-06-14T16:58:04Z)
• Geometry and quantum brachistochrone analysis of multiple entangled spin-1/2 particles under all-range Ising interaction [0.0]
  We present a unified geometric and dynamical framework for a physical system consisting of $n$ spin-$1/2$ particles with all-range Ising interaction.<n>Our analysis reveals that the system evolves over a smooth, compact, two-dimensional manifold with spherical topology.<n>We explore the role of entanglement in shaping the state space geometry, modulating geometric phase, and controlling evolution speed and brachistochrone time.
  arXiv  Detail & Related papers  (2025-12-24T19:37:07Z)
• Evolution of multi-qubit correlations driven by mutual interactions [49.1574468325115]
  We analyze the evolution of the correlation tensor elements of quantum systems composed of $frac12$-spins.<n>We show how a strong external field can play a stabilizing factor with respect to certain correlation characteristics.
  arXiv  Detail & Related papers  (2025-07-01T11:45:08Z)
• Meson spectroscopy of exotic symmetries of Ising criticality in Rydberg atom arrays [39.58317527488534]
  Coupling two Ising chains in a ladder leads to an even richer $mathcalD(1)_8$ symmetries.<n>Here, we probe these emergent symmetries in a Rydberg atom processing unit, leveraging its geometry to realize both chain and ladder configurations.
  arXiv  Detail & Related papers  (2025-06-26T14:19:30Z)
• Hilbert space geometry and quantum chaos [39.58317527488534]
  We consider the symmetric part of the QGT for various multi-parametric random matrix Hamiltonians. We find for a two-dimensional parameter space that, while the ergodic phase corresponds to the smooth manifold, the integrable limit marks itself as a singular geometry with a conical defect.
  arXiv  Detail & Related papers  (2024-11-18T19:00:17Z)
• Measurement-induced transitions for interacting fermions [43.04146484262759]
  We develop a field-theoretical framework that provides a unified approach to observables characterizing entanglement and charge fluctuations.<n>Within this framework, we derive a replicated Keldysh non-linear sigma model (NLSM)<n>By using the renormalization-group approach for the NLSM, we determine the phase diagram and the scaling of physical observables.
  arXiv  Detail & Related papers  (2024-10-09T18:00:08Z)
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [43.80709028066351]
  Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system.<n>This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
  arXiv  Detail & Related papers  (2023-10-04T09:51:00Z)
• Complementarity between quantum entanglement, geometrical and dynamical appearances in N spin-$1/2$ system under all-range Ising model [0.0]
  Modern geometry studies the interrelations between elements such as distance and curvature. We explore these structures in a physical system of $N$ interaction spin-$1/2$ under all-range Ising model.
  arXiv  Detail & Related papers  (2023-04-11T15:26:19Z)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• Geometrical, topological and dynamical description of $\mathcal{N}$ interacting spin-$\mathtt{s}$ under long-range Ising model and their interplay with quantum entanglement [0.0]
  This work investigates the connections between integrable quantum systems with quantum phenomena exploitable in quantum information tasks. We find the relevant dynamics, identify the corresponding quantum phase space and derive the associated Fubini-Study metric. By narrowing the system to a two spin-$mathtts$ system, we explore the relevant entanglement from two different perspectives.
  arXiv  Detail & Related papers  (2022-10-29T11:53:14Z)

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.