Strong convergence of a resolution of the identity via canonical coherent states

• URL: http://arxiv.org/abs/2402.08317v1
• Date: Tue, 13 Feb 2024 09:25:22 GMT
• Title: Strong convergence of a resolution of the identity via canonical coherent states
• Abstract summary: A resolution of the identity due to canonical coherent states is often proven in the weak operator topology. We show that the relevant uniform limit does not exist.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A resolution of the identity due to canonical coherent states is often proven in the weak operator topology. However, such a resolution with an integral symbol is typically supposed to hold in the strong operator topology associated with the framework of the spectral theorem. We provide an elementary proof of the strong convergence for the resolution of the identity due to canonical coherent states starting with a mostly familiar setup. Further, we enjoy a different proof and show that the relevant uniform limit does not exist.

Related papers

• The Resolution of the Identity as a Generator of Exact Integral Identities: A Coherent-State Approach [0.0]
  We show that the resolution of the identity associated with Glauber coherent states is a direct generator of exact complex Gaussian integral identities.<n>We highlight an intriguing non-commuting behavior in the parameter limits of the master identity.<n>This approach offers a transparent and visually intuitive illustration of how Hilbert-space completeness inherently encodes vast libraries of exact, solvable mathematical relations.
  arXiv  Detail & Related papers  (2026-07-14T14:35:09Z)
• Non-Hermitian topology driven by an identity term: An exactly solvable paradigm [11.093624836836929]
  We show that a momentum-dependent identity term actively deforms the generalized Brillouin zone under non-Hermitian skin pumping.<n>This work establishes an exactly solvable paradigm for non-Hermitian topology beyond symmetry protection.
  arXiv  Detail & Related papers  (2026-07-09T13:27:07Z)
• Unsupervised Disentanglement Without Compromises : How Functional Orthogonality Enforces Identifiability [46.784084625532984]
  This paper explores unsupervised disentangled representation learning from a functional perspective.<n>We prove that this condition yields identifiability of general nonlinear generative models.
  arXiv  Detail & Related papers  (2026-06-19T12:47:07Z)
• The Wittgensteinian Representation Hypothesis: Is Language the Attractor of Multimodal Convergence? [37.415683554349194]
  We introduce directional convergence analysis using cycle-kNN, an asymmetric alignment measure.<n>Non-language modalities move toward the neighborhood structure of language significantly more than the reverse.<n>We formalize this as the Wittgensteinian Representation Hypothesis: the semantic structure of language is the attractor of multimodal representation convergence.
  arXiv  Detail & Related papers  (2026-05-10T06:05:04Z)
• Beyond ReLU: Bifurcation, Oversmoothing, and Topological Priors [28.452964044443906]
  Graph Neural Networks (GNNs) learn node representations through iterative network-based message-passing.<n>Deep GNNs suffer from oversmoothing, where node features converge to a homogeneous, non-informative state.<n>We re-frame this problem of representational collapse from a emphbifurcation theory perspective, characterizing oversmoothing as convergence to a stable homogeneous fixed point.
  arXiv  Detail & Related papers  (2026-02-17T15:03:28Z)
• A Formal Proof of a Continued Fraction Conjecture for $π$ Originating from the Ramanujan Machine [2.579369112489757]
  We provide a formal analytic proof for a class of non-canonical continued fractions representing /4.<n>We show that these identities can be derived via a discrete sequence of equivalence transformations.<n>This work demonstrates that such algorithmically discovered identities are not isolated numerical artifacts, but are deeply rooted in the classical theory of hypergeometric transformations.
  arXiv  Detail & Related papers  (2026-01-13T11:38:44Z)
• Exponential convergence rate for Iterative Markovian Fitting [58.760054965084656]
  Iterative Markovian Fitting (IMF) algorithm converges in Kullback-Leibler divergence to the ground truth solution.<n>We establish for the first time that IMF exhibits exponential convergence with an explicit contraction factor.
  arXiv  Detail & Related papers  (2025-08-04T09:48:21Z)
• Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory [0.0]
  This paper contributes to the Alpay Algebra by demonstrating that the stable outcome of a self referential process is identical to the unique equilibrium of an unbounded revision dialogue between a system and its environment.<n>By unifying concepts from fixed point theory, game semantics, ordinal analysis, and type theory, this research establishes a broadly accessible yet formally rigorous foundation for reasoning about infinite self referential systems.
  arXiv  Detail & Related papers  (2025-07-25T13:12:55Z)
• Multi-state imaginarity and coherence in qubit systems [3.7112567233163003]
  We provide a unitary-invariant framework to pinpoint imaginarity and coherence in sets of qubit states.<n>We also show that the set of imaginarity-free multi-states is not convex, and that third-order invariants completely characterize multi-state imaginarity of single-qubits but not of higher-dimensional systems.
  arXiv  Detail & Related papers  (2025-07-20T09:34:57Z)
• Improving absolute separability bounds for arbitrary dimensions [0.0]
  Sufficient analytical conditions for separability in composite quantum systems are very scarce and only known for low-dimensional cases. We use linear maps and their inverses to derive powerful analytical conditions, providing tight bounds and extremal points of the set of absolutely separable states.
  arXiv  Detail & Related papers  (2024-10-29T18:00:04Z)
• C$^3$DG: Conditional Domain Generalization for Hyperspectral Imagery Classification with Convergence and Constrained-risk Theories [23.21421412818663]
  Hyperspectral imagery (HSI) classification may suffer the challenge of hyperspectral-monospectra. Joint spatial-spectral feature extraction is a popular solution for the problem. We propose a Convergence and Error-Constrained Conditional Domain Generalization method.
  arXiv  Detail & Related papers  (2024-07-04T18:03:45Z)
• A new class of exact coherent states: enhanced quantization of motion on the half-line [0.16385815610837165]
  We find a class of dynamically stable coherent states for motion on the half-line. The regularization of the half-line boundary and the consequent quantum motion are expounded within the framework of covariant affine quantization. Our discovery holds significant relevance in the field of quantum cosmology.
  arXiv  Detail & Related papers  (2023-10-25T13:19:24Z)
• Generalization Guarantees via Algorithm-dependent Rademacher Complexity [33.408679482592426]
  We propose a measure to control generalization error, which is the empirical Rademacher complexity of an algorithm- and data-dependent hypothesis class. We obtain novel bounds based on the finite fractal dimension, which (a) extend previous fractal-type bounds from continuous to finite hypothesis classes, and (b) avoid a mutual information term.
  arXiv  Detail & Related papers  (2023-07-04T18:37:38Z)
• Unextendibility, uncompletability, and many-copy indistinguishable ensembles [77.34726150561087]
  We study unextendibility, uncompletability and analyze their connections to many-copy indistinguishable ensembles. We report a class of multipartite many-copy indistinguishable ensembles for which local indistinguishability property increases with decreasing mixedness.
  arXiv  Detail & Related papers  (2023-03-30T16:16:41Z)
• Error bounds for Lie Group representations in quantum mechanics [44.99833362998488]
  We provide state-dependent error bounds for strongly continuous unitary representations of Lie groups. Our method works for any connected Lie group and the metric is independent of the chosen representation.
  arXiv  Detail & Related papers  (2022-11-15T23:55:53Z)
• A non-graphical representation of conditional independence via the neighbourhood lattice [24.187900567260577]
  We show that this decomposition exists in any compositional graphoid and can be computed efficiently and consistently in high-dimensions. We also discuss various special cases such as graphical models and projection lattices, each of which has intuitive interpretations.
  arXiv  Detail & Related papers  (2022-06-12T19:59:09Z)
• Pseudo standard entanglement structure cannot be distinguished from standard entanglement structure [61.12008553173672]
  An experimental verification of the maximally entangled state does not guarantee that the state is exactly the same as the maximally entangled state. In our setting, any maximally entangled state can be arbitrarily approximated by an entangled state that belongs to our obtained pseudo standard entanglement structure.
  arXiv  Detail & Related papers  (2022-03-15T14:56:43Z)
• Bayesian Consistency with the Supremum Metric [13.769786711365104]
  A key result of the paper is that we demonstrate supremum consistency using weaker conditions compared to those currently used to secure $mathbbL_1$ consistency.
  arXiv  Detail & Related papers  (2022-01-10T16:39:25Z)
• Coherent States for infinite homogeneous waveguide arrays: Cauchy coherent states for $E(2)$ [0.0]
  Perelomov coherent states for infinite homogeneous waveguide arrays with Euclidean E(2) symmetry are defined. It is shown that Perelomov coherent states for the Eucliean E(2) group have a simple and natural physical realization.
  arXiv  Detail & Related papers  (2021-12-01T22:51:53Z)
• Non-standard entanglement structure of local unitary self-dual models as a saturated situation of repeatability in general probabilistic theories [61.12008553173672]
  We show the existence of infinite structures of quantum composite system such that it is self-dual with local unitary symmetry. We also show the existence of a structure of quantum composite system such that non-orthogonal states in the structure are perfectly distinguishable.
  arXiv  Detail & Related papers  (2021-11-29T23:37:58Z)
• Comment on "Strong Quantum Darwinism and Strong Independence are Equivalent to Spectrum Broadcast Structure" [62.997667081978825]
  We show that the mathematical formulation of condition (b) is necessary but not sufficient to ensure the equivalence. We propose a simple counter-example, together with a strengthened formulation of condition (b)
  arXiv  Detail & Related papers  (2021-01-21T16:06:25Z)
• Generalized Susskind-Glogower coherent states [0.3149883354098941]
  We introduce two new families of Susskind-Glogower-I and Susskind-Glogower-II coherent states. For completeness, the optical properties related to the new families of coherent states are explored and compared with respect to some well-known optical states.
  arXiv  Detail & Related papers  (2020-11-20T09:55:49Z)
• A Weaker Faithfulness Assumption based on Triple Interactions [89.59955143854556]
  We propose a weaker assumption that we call $2$-adjacency faithfulness. We propose a sound orientation rule for causal discovery that applies under weaker assumptions.
  arXiv  Detail & Related papers  (2020-10-27T13:04:08Z)
• Quantum Geometric Confinement and Dynamical Transmission in Grushin Cylinder [68.8204255655161]
  We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder. We retrieve those distinguished extensions previously identified in the recent literature, namely the most confining and the most transmitting.
  arXiv  Detail & Related papers  (2020-03-16T11:37:23Z)

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.