Asymptotic statistical theory of irreducible quantum Markov chains

• URL: http://arxiv.org/abs/2603.20761v1
• Date: Sat, 21 Mar 2026 11:16:39 GMT
• Title: Asymptotic statistical theory of irreducible quantum Markov chains
• Abstract summary: We show that the space of identifiable parameters for the stationary output is a space called an orbifold.<n>We show that the joint system and output model satisfies quantum local normality.<n>We provide an in-depth analysis of the model with smallest dimensions, consisting of two-dimensional system and environment units.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper we investigate the asymptotic statistical theory of irreducible quantum Markov chains, focusing on identifiability properties and asymptotic convergence of associated quantum statistical models. We show that the space of identifiable parameters for the stationary output is a stratified space called an orbifold, which is obtained as the quotient of the manifold of irreducible dynamics by a compact group of state preserving symmetries. We analyse the orbifold's geometric properties, the connection between periodicity and strata, and provide orbifold charts as the starting point for the local asymptotic theory. The quantum Fisher information rate of the system and output state is expressed in terms of a canonical inner product on the identifiable tangent space. We then show that the joint system and output model satisfies quantum local asymptotic normality while the stationary output model converges to a product between a quantum Gaussian shift model and a mixture of quantum Gaussian shift models, reflecting the underlying periodicity. These strong convergence results provide the basis for constructing asymptotically optimal estimators of dynamical parameters. We provide an in-depth analysis of the model with smallest dimensions, consisting of two-dimensional system and environment units.

Related papers

• Quantum spectroscopy of topological dynamics via a supersymmetric Hamiltonian [0.0]
  We estimate topological descriptors through quantum spectroscopy.<n>We show that low-lying excited states quantify the stability of topological features.<n>This framework suggests that quantum hardware can function as a spectrometer for data topologies beyond classical reach.
  arXiv  Detail & Related papers  (2025-11-28T13:25:26Z)
• Classical feature map surrogates and metrics for quantum control landscapes [0.0]
  We derive and analyze three feature maps of parametrized quantum dynamics, which generalize variational quantum circuits.<n>The Lie-Fourier representation is shown to have a dense spectrum with discrete peaks, that reflects control Hamiltonian properties, but that is compressible in typically found symmetric systems.
  arXiv  Detail & Related papers  (2025-09-30T08:24:13Z)
• Symmetry-adapted sample-based quantum diagonalization: Application to lattice model [0.0]
  We present a symmetry-adapted extension of sample-based quantum diagonalization (SQD) that embeds space-group symmetry into the many-body subspace sampled by quantum hardware.<n>The method is benchmarked on the two-leg ladder Hubbard model using both molecular orbital and momentum bases.
  arXiv  Detail & Related papers  (2025-05-01T23:23:37Z)
• Exploring entanglement in finite-size quantum systems with degenerate ground state [0.0]
  We develop an approach for characterizing non-local quantum correlations in spin systems with exactly or nearly degenerate ground states.<n> Estimating the von Neumann entropy of the random wave functions helps to reveal previously unknown features of the quantum correlations in the phases with degeneracy of the ground state.<n>Digital quantum simulations performed with quantum computers can provide accurate description of the entanglement of the degenerate systems even in the presence of noise.
  arXiv  Detail & Related papers  (2024-10-01T08:56:34Z)
• 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)
• Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations [114.17826109037048]
  Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning. theoretical aspects, e.g., identifiability and properties of statistical estimation are still obscure. This paper derives a sufficient condition for the identifiability of homogeneous linear ODE systems from a sequence of equally-spaced error-free observations sampled from a single trajectory.
  arXiv  Detail & Related papers  (2022-10-12T06:46:38Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• Hilbert-space geometry of random-matrix eigenstates [55.41644538483948]
  We discuss the Hilbert-space geometry of eigenstates of parameter-dependent random-matrix ensembles. Our results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature. We compare our results to numerical simulations of random-matrix ensembles as well as electrons in a random magnetic field.
  arXiv  Detail & Related papers  (2020-11-06T19:00:07Z)
• Long-range level correlations in quantum systems with finite Hilbert space dimension [0.0]
  We study the spectral statistics of quantum systems with finite Hilbert spaces. We derive a theorem showing that eigenlevels in such systems cannot be globally uncorrelated.
  arXiv  Detail & Related papers  (2020-10-13T15:49:15Z)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)

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.