Irreducibility and regularisation properties of Gaussian quantum Markov semigroups

• URL: http://arxiv.org/abs/2609.01547v1
• Date: Tue, 01 Sep 2026 17:14:48 GMT
• Title: Irreducibility and regularisation properties of Gaussian quantum Markov semigroups
• Abstract summary: We study regularisation and irreducibility properties of GQMSs acting on continuous-variable quantum systems.<n>A central and surprising consequence is that, in contrast with the classical case, irreducibility is strictly stronger than conditions ensuring regularisation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study regularisation and irreducibility properties of Gaussian quantum Markov semigroups (GQMSs) acting on continuous-variable quantum systems. We first identify a natural notion of regularity for operators in this setting, which allows us to formulate and characterise the smoothing effects of GQMSs in terms of algebraic conditions involving the drift and quantum diffusion matrices. These conditions establish a connection with the controllability theory of quantum linear systems and with the structure of decoherence-free subsystems. We then characterise irreducibility through several equivalent algebraic criteria: one formulated in terms of the drift and quantum diffusion matrices, one in terms of the operators appearing in the generalised GKLS representation of the generator, and a third given by a quantum analogue of Hörmander's condition. A central and somewhat surprising consequence is that, in contrast with the classical case, irreducibility is strictly stronger than conditions ensuring regularisation. Our results provide an algebraic framework for analysing these properties and lay the groundwork for a broader study of reducible Gaussian quantum Markov semigroups and, more generally, more general relevant quantum Markov semigroups on continuous-variable systems.

Related papers

• Typical entanglement in anyon chains: Page curves beyond Lie group symmetries [41.99844472131922]
  We study bipartite entanglement statistics in one-dimensional anyon chains constrained by fusion rules of unitary pre-modular categories.<n>Surprisingly, despite the constrained Hilbert space structure, the large $L$ expansion has no universal $O(sqrtL)$ or $O(1)$ symmetry-type corrections.<n> Numerical simulations of the integrable and quantum-chaotic golden chain Hamiltonian show that chaotic mid-spectrum eigenstates match the Haar-random predictions.
  arXiv  Detail & Related papers  (2026-03-26T18:00:03Z)
• Hysteretic squashed entanglement in many-body quantum systems [42.085941481155295]
  Entanglement in many-body quantum systems is distributed across spatial regions.<n>We propose hysteretic entanglement $T_sq$, a conditional entanglement that measures the genuine quantum correlations between two subregions.<n>We show that $T_sq$ can detect genuine quantum correlations across both adjacent and long-range subsystems.
  arXiv  Detail & Related papers  (2026-03-10T17:00:49Z)
• Characterizing Trainability of Instantaneous Quantum Polynomial Circuit Born Machines [7.716642023459826]
  Instantaneous quantum quantum circuit Born machines (IQP-QCBMs) have been proposed as quantum generative models.<n>We show that barren plateaus depend on the generator set and the spectrum of the chosen kernel.<n>We identify regimes in which low-weight-biased kernels avoid exponential suppression in structured topologies.
  arXiv  Detail & Related papers  (2026-02-11T17:12:56Z)
• Random matrix theory universality of current operators in spin-$S$ Heisenberg chains [0.0]
  We study the conjecture numerically in translationally invariant Heisenberg spin chains with spin quantum number $S =frac12,1,frac32$.<n>Our findings further support the conjecture of the existence of RMT universality as manifest in the observable properties in quantum chaotic systems.
  arXiv  Detail & Related papers  (2026-01-15T09:23:48Z)
• Gaussian quantum Markov semigroups on finitely many modes admitting a normal invariant state [0.0]
  Gaussian quantum Markov semigroups (GQMSs) are of fundamental importance in modelling the evolution of several quantum systems.<n>We completely characterize those GQMSs that admit a normal invariant state and we provide a description of the set of normal invariant states.<n>We study the behavior of such semigroups for long times: firstly, we clarify the relationship between the decoherence-free subalgebra and the spectrum of $mathbfZ$.
  arXiv  Detail & Related papers  (2024-12-13T10:01:18Z)
• Precision bounds for multiple currents in open quantum systems [37.69303106863453]
  We derivation quantum TURs and KURs for multiple observables in open quantum systems undergoing Markovian dynamics.<n>Our bounds are tighter than previously derived quantum TURs and KURs for single observables.<n>We also find an intriguing quantum signature of correlations captured by the off-diagonal element of the Fisher information matrix.
  arXiv  Detail & Related papers  (2024-11-13T23:38:24Z)
• How Much Entanglement Is Needed for Topological Codes and Mixed States with Anomalous Symmetry? [9.27220088595816]
  We provide quantitative characterizations of entanglement necessary for emergent anyons and fermions.<n>For systems with emergent fermions, despite that the ground state subspaces could be exponentially huge, we show that the GEM also scales linearly in the system size.<n>Our analysis establishes an intriguing link between quantum anomaly and entanglement.
  arXiv  Detail & Related papers  (2024-05-13T17:47:15Z)
• Unleashed from Constrained Optimization: Quantum Computing for Quantum Chemistry Employing Generator Coordinate Inspired Method [9.95432381301196]
  We introduce an adaptive scheme that robustly constructs the many-body basis sets from a pool of the Unitary Coupled Cluster excitation generators.<n>This scheme supports the development of a hierarchical ADAPT quantum-classical strategy, enabling a balanced interplay between subspace expansion and ansatz optimization.
  arXiv  Detail & Related papers  (2023-12-12T19:36:51Z)
• Energy preserving evolutions over Bosonic systems [1.7478203318226315]
  We investigate perturbations of quantum dynamical semigroups that operate on continuous variable systems.<n>We provide a new scheme for deriving continuity bounds on the energy-constrained capacities of Markovian perturbations of quantum dynamical semigroups.
  arXiv  Detail & Related papers  (2023-07-25T20:13:30Z)
• Hybrid quantum-classical systems: Quasi-free Markovian dynamics [0.0]
  In the case of a quantum-classical hybrid system, the problem of characterizing the most general dynamical semigroup is solved under the restriction of being quasi-free. We show how to extract multi-time probabilities and how to connect them to the quantum notions of positive operator valued measure and instrument. A concrete example is given, showing how a classical component can input noise into a quantum one and how the classical system can extract information on the behaviour of the quantum one.
  arXiv  Detail & Related papers  (2023-07-05T19:26:09Z)
• Quantum algorithms for generator coordinate methods [12.744157326232749]
  This paper discusses quantum algorithms for the generator coordinate method (GCM) that can be used to benchmark molecular systems. We illustrate the performance of the quantum algorithm for constructing a discretized form of the Hill-Wheeler equation for ground and excited state energies.
  arXiv  Detail & Related papers  (2022-12-19T01:22:19Z)
• Complete entropic inequalities for quantum Markov chains [17.21921346541951]
  We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional algebra satisfies a modified log-Sobolev inequality. We also establish the first general approximateization property of relative entropy.
  arXiv  Detail & Related papers  (2021-02-08T11:47:37Z)
• A Wigner-Eckart Theorem for Group Equivariant Convolution Kernels [16.143012623830792]
  Group equivariant convolutional networks (GCNNs) endow classical convolutional networks with additional symmetry priors. Recent advances in the theoretical description of GCNNs revealed that such models can generally be understood as performing convolutions with G-steerable kernels.
  arXiv  Detail & Related papers  (2020-10-21T12:42:23Z)
• Extremal quantum states [0.41998444721319206]
  We peruse quantumness from a variety of viewpoints, concentrating on phase-space formulations. The symmetry-transcending properties of the Husimi $Q$ function make it our basic tool. We use these quantities to formulate extremal principles and determine in this way which states are the most and least "quantum"
  arXiv  Detail & Related papers  (2020-10-09T18:00:02Z)

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.