Irreducibility of Quantum Markov Semigroups, uniqueness of invariant states and related properties

• URL: http://arxiv.org/abs/2512.11517v1
• Date: Fri, 12 Dec 2025 12:33:07 GMT
• Title: Irreducibility of Quantum Markov Semigroups, uniqueness of invariant states and related properties
• Authors: Franco Fagnola, Federico Girotti,
• Abstract summary: We show that irreducibility, primitivity and relaxation towards a faithful invariant density are equivalent when the semigroup admits an invariant density.<n>In the case of uniformly continuous QMSs, we present several useful ways of checking irreducibility in terms of the operators appearing in the generator in GKLS form.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present different characterizations of the notion of irreducibility for Quantum Markov Semigroups (QMSs) and investigate its relationship with other relevant features of the dynamics, such as primitivity, positivity improvement and relaxation; in particular, we show that irreducibility, primitivity and relaxation towards a faithful invariant density are equivalent when the semigroup admits an invariant density. Moreover, in the case of uniformly continuous QMSs, we present several useful ways of checking irreducibility in terms of the operators appearing in the generator in GKLS form. Our exposition is as much self-contained as possible, we present some well known results with elementary proofs (collecting all the relevant literature) and we derive new ones. We study both finite and infinite dimensional evolutions and we remark that many results only require the QMS to be made of Schwarz maps.

Related papers

• 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)
• Unifying inequalities bounding quantum speed limits [0.0]
  We investigate the role of generalized fidelity measures in the derivation of quantum speed limits (QSLs)<n>We show that the resulting Margolus-Levitin and Mandelstam-Tamm bounds for both unitary and non-unitary dynamics depend solely on the chosen fidelity measure.
  arXiv  Detail & Related papers  (2025-09-04T14:58:36Z)
• Grassmann Variational Monte Carlo with neural wave functions [45.935798913942904]
  We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
  arXiv  Detail & Related papers  (2025-07-14T13:53:13Z)
• Geometric Invariants of Quantum Metrology [0.0]
  We show a previously unexplored conservation law for the Quantum Fisher Information Matrix.<n>Lie algebras endow any quantum state with a fixed "budget" of metrological sensitivity.<n>We discuss this as it relates to the quantum analogs of classical optimality criteria.
  arXiv  Detail & Related papers  (2025-07-08T16:15:19Z)
• Dissipation-Induced Threshold on Integrability Footprints [1.0159681653887238]
  We study how signatures of integrability fade as dissipation strength increases.<n>We estimate the critical dissipation threshold beyond which these clusters disappear.<n>Our results provide a quantitative picture of how noise gradually erases the footprints of integrability in open quantum systems.
  arXiv  Detail & Related papers  (2025-04-14T14:16:37Z)
• Predicting symmetries of quantum dynamics with optimal samples [41.42817348756889]
  Identifying symmetries in quantum dynamics is a crucial challenge with profound implications for quantum technologies.<n>We introduce a unified framework combining group representation theory and subgroup hypothesis testing to predict these symmetries with optimal efficiency.<n>We prove that parallel strategies achieve the same performance as adaptive or indefinite-causal-order protocols.
  arXiv  Detail & Related papers  (2025-02-03T15:57:50Z)
• A unified framework of unitarily residual measures for quantifying dissipation [1.6574413179773757]
  We introduce a framework for quantifying the dissipation by isolating the non-unitary components of quantum dynamics.<n>Our results provide a powerful tool for quantifying dissipation in open quantum systems, advancing the understanding of quantum thermodynamics.
  arXiv  Detail & Related papers  (2024-12-03T08:00:24Z)
• 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)
• Entanglement monogamy via multivariate trace inequalities [12.814476856584346]
  We derive variational formulas for relative entropies based on restricted measurements of multipartite quantum systems. We give direct, matrix-analysis-based proofs for the faithfulness of squashed entanglement.
  arXiv  Detail & Related papers  (2023-04-28T14:36:54Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• 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)
• On the complex behaviour of the density in composite quantum systems [62.997667081978825]
  We study how the probability of presence of a particle is distributed between the two parts of a composite fermionic system. We prove that it is a non-perturbative property and we find out a large/small coupling constant duality. Inspired by the proof of KAM theorem, we are able to deal with this problem by introducing a cut-off in energies that eliminates these small denominators.
  arXiv  Detail & Related papers  (2020-04-14T21:41:15Z)

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.