Quantum Reference Frames on Homogeneous Spaces
- URL: http://arxiv.org/abs/2409.07231v1
- Date: Wed, 11 Sep 2024 12:44:34 GMT
- Title: Quantum Reference Frames on Homogeneous Spaces
- Abstract summary: Properties of operator-valued integration are first studied and then employed to define general relativization maps and show their properties.
The relativization maps presented here are defined for QRFs based on arbitrary homogeneous spaces of locally compact second countable topological groups.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: This paper initiates a systematic study of operators arising as integrals of operator-valued functions with respect to positive operator-valued measures and utilizes these tools to provide relativization maps (Yen) for quantum reference frames (QRFs) defined on general homogeneous spaces. Properties of operator-valued integration are first studied and then employed to define general relativization maps and show their properties. The relativization maps presented here are defined for QRFs (systems of covariance) based on arbitrary homogeneous spaces of locally compact second countable topological groups and are shown to be contracting quantum channels, injective for localizable (norm-1 property) frames and multiplicative for the sharp ones (PVMs), extending the existing results.
Related papers
- Irreducibility and regularisation properties of Gaussian quantum Markov semigroups [0.0]
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.
arXiv Detail & Related papers (2026-09-01T17:14:48Z) - Spectral graph clustering with inhomogeneous latent geometry [42.02177719060884]
We develop a density-based spectral clustering algorithm that requires only approximate localization of the informative eigenvalue.<n>Our theoretical predictions for the location of the informative eigenvalue notably align with observations in real-world experiments.
arXiv Detail & Related papers (2026-08-11T18:15:38Z) - Nested Integral Generator Theorem: From Operator Tautologies to Families of Exact Integral Identities [0.0]
An exact integral representation of a Kerr-squeezed coherent-state overlap and exact Fock-basis elements for a composite two-mode Gaussian network is presented.<n>The taut theorem yields exact representations for individual operator functions.<n>Its scope is illustrated through elementary, analytic and single-mode operators, as well as single- and two-mode unitaries, including squeezing and beam splitting.
arXiv Detail & Related papers (2026-07-25T14:53:28Z) - Spatial Localization of Relativistic Quantum Systems: The Commutativity Requirement and the Locality Principle. Part II: A Model from Local QFT [0.0]
We construct a class of positive-energy relativistic spatial localization observables in Minkowski spacetime.<n>For each timelike direction, the construction yields a family of positive operator-valued measures (POVMs) on spacelike hypersurfaces.<n>These observables arise from local or quasi-local field-theoretic quantities.
arXiv Detail & Related papers (2026-04-05T16:34:37Z) - RKHS Representation of Algebraic Convolutional Filters with Integral Operators [111.57971404925486]
In this paper, we develop a theory showing that the range of integral operators naturally induces RKHS convolutional signal models.<n>We show that filtering with integral operators corresponds to iterated box products, giving rise to a unital kernel algebra.<n>Our results establish precise connections between eigendecompositions and RKHS representations in graphon signal processing, extend naturally to directed graphons, and enable novel spatial-spectral localization results.
arXiv Detail & Related papers (2026-02-22T08:28:34Z) - Quantum Monads in Phase Space and Related Toeplitz Operators [0.0]
In earlier work, we introduced quantum blobs as minimum-uncertainty symplectic ellipsoids in phase space.<n>These objects may be viewed as geometric monads in the Leibnizian sense.<n>We establish a one-to-one correspondence between such monads and generalized coherent states.
arXiv Detail & Related papers (2025-11-09T18:32:18Z) - Topological Tenfold Classification and the Entanglement of Two Qubits [0.0]
We use the Cartan decomposition to characterize topological properties and their connection to quantum entanglement.
Topological features are obtained systematically by a mapping to a quantum graph.
An additional perspective is provided regarding the extension of this new approach to condensed matter systems.
arXiv Detail & Related papers (2025-02-04T15:47:19Z) - Learning convolution operators on compact Abelian groups [35.70694383605516]
We consider the problem of learning convolution operators associated to compact Abelian groups.<n>We study a regularization-based approach and provide learning guarantees under natural regularity conditions.
arXiv Detail & Related papers (2025-01-09T14:43:08Z) - Integral quantization based on the Heisenberg-Weyl group [39.58317527488534]
We develop a framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime.<n>The proposed scheme is based on coherent states generated by the action of the Heisenberg-Weyl group.<n>A direct application of our model, including a computation of transition amplitudes between states characterized by fixed positions and momenta, is postponed to a forthcoming article.
arXiv Detail & Related papers (2024-10-31T14:36:38Z) - Relativization is naturally functorial [0.0]
We provide some categorical perspectives on the relativization construction arising from quantum measurement theory.
This construction provides, for any quantum system, a quantum channel from the system's algebra to the invariant algebra on the composite system.
arXiv Detail & Related papers (2024-03-06T14:42:22Z) - Covariant operator bases for continuous variables [0.0]
We work out an alternative basis consisting of monomials on the basic observables, with the crucial property of behaving well under symplectic transformations.
Given the density matrix of a state, the expansion coefficients in that basis constitute the multipoles, which describe the state in a canonically covariant form that is both concise and explicit.
arXiv Detail & Related papers (2023-09-18T18:00:15Z) - Remarks on the quasi-position representation in models of generalized
uncertainty principle [0.0]
This note aims to elucidate certain aspects of the quasi-position representation frequently used in the investigation of one-dimensional models.
We focus on two key points: (i) Contrary to recent claims, the quasi-position operator can possess physical significance even though it is non-Hermitian, and (ii) in the quasi-position representation, operators associated with the position behave as a derivative operator on the quasi-position coordinate.
arXiv Detail & Related papers (2023-06-20T11:46:56Z) - Optimal Semiclassical Regularity of Projection Operators and Strong Weyl
Law [0.0]
We prove that projection operators converge to characteristic functions of the phase space.
This can be interpreted as a semiclassical on the size of commutators in Schatten norms.
arXiv Detail & Related papers (2023-02-09T18:05:17Z) - Reinforcement Learning from Partial Observation: Linear Function Approximation with Provable Sample Efficiency [111.83670279016599]
We study reinforcement learning for partially observed decision processes (POMDPs) with infinite observation and state spaces.
We make the first attempt at partial observability and function approximation for a class of POMDPs with a linear structure.
arXiv Detail & Related papers (2022-04-20T21:15:38Z) - Self-adjoint extension schemes and modern applications to quantum
Hamiltonians [55.2480439325792]
monograph contains revised and enlarged materials from previous lecture notes of undergraduate and graduate courses and seminars delivered by both authors over the last years on a subject that is central both in abstract operator theory and in applications to quantum mechanics.
A number of models are discussed, which are receiving today new or renewed interest in mathematical physics, in particular from the point of view of realising certain operators of interests self-adjointly.
arXiv Detail & Related papers (2022-01-25T09:45:16Z) - Finite-Function-Encoding Quantum States [52.77024349608834]
We introduce finite-function-encoding (FFE) states which encode arbitrary $d$-valued logic functions.
We investigate some of their structural properties.
arXiv Detail & Related papers (2020-12-01T13:53:23Z) - 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) - Relevant OTOC operators: footprints of the classical dynamics [68.8204255655161]
The OTOC-RE theorem relates the OTOCs summed over a complete base of operators to the second Renyi entropy.
We show that the sum over a small set of relevant operators, is enough in order to obtain a very good approximation for the entropy.
In turn, this provides with an alternative natural indicator of complexity, i.e. the scaling of the number of relevant operators with time.
arXiv Detail & Related papers (2020-07-31T19:23:26Z) - Quasi-probability distributions in Loop Quantum Cosmology [0.0]
We introduce a complete family of parametrized quasi-probability distributions in phase space and their corresponding Weyl quantization maps.
We expect our results may serve to analyze several fundamental aspects within the Loop Quantum Cosmology program.
arXiv Detail & Related papers (2020-07-02T18:05:32Z) - Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range.
For a large part of the presentation, infinite scattering length will be considered.
arXiv Detail & Related papers (2020-06-03T17:54:43Z)
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.