Alternative commutation relations, star products and tomography

DOI10.1088/0305-4470/35/3/315zbMath1041.81080arXivquant-ph/0112110OpenAlexW2076062749MaRDI QIDQ4465571

Giuseppe Marmo, Vladimir I. Man'ko, Olga V. Man'ko

Publication date: 9 June 2004

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0112110

Mathematics Subject Classification ID

Geometry and quantization, symplectic methods (81S10) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Deformation quantization, star products (53D55)

Related Items (35)

Tomographic portrait of quantum channels ⋮ Star product, discrete Wigner functions, and spin-system tomograms ⋮ Classical and quantum systems: alternative Hamiltonian descriptions ⋮ Similarity transformations of Hermitian Hamiltonians and pseudo-Hermitian coupling between two electromagnetic modes ⋮ Minimal sets of dequantizers and quantizers for finite-dimensional quantum systems ⋮ ALTERNATIVE LINEAR STRUCTURES FOR CLASSICAL AND QUANTUM SYSTEMS ⋮ Center of mass tomography for reconstructing quantum states of multipartite systems ⋮ Observables, interference phenomenon and Born’s rule in the probability representation of quantum mechanics ⋮ On the tomographic description of classical fields ⋮ Robustness of raw quantum tomography ⋮ Observables, evolution equation, and stationary states equation in the joint probability representation of quantum mechanics ⋮ Semigroup of positive maps for qudit states and entanglement in tomographic probability representation ⋮ Quantizer-dequantizer operators as a tool for formulating the quantization procedure ⋮ On various functional representations of the space of Schwartz operators ⋮ Remarks on the star product of functions on finite and compact groups ⋮ Gauge transformation of quantum states in probability representation ⋮ Integral transforms between tomogram and quasi-probability functions based on quantizer-dequantizer operators formalism ⋮ Tomograms in the quantum-classical transition ⋮ Tomographic entropy and cosmology ⋮ New inequalities for tomograms in the probability representation of quantum states ⋮ Phase space distributions and a duality symmetry for star products ⋮ Star products, duality and double Lie algebras ⋮ Quadratic tomography star product algebra and its classical limit ⋮ Quantum tomography and the quantum Radon transform ⋮ On the inversion of the Radon transform: standard versusM²approach ⋮ Quasi-probability distributions in loop quantum cosmology ⋮ Positive maps of density matrix and a tomographic criterion of entanglement ⋮ On the meaning and interpretation of tomography in abstract Hilbert spaces ⋮ f-oscillators deformation for Moyal algebras ⋮ Center-of-mass tomographic approach to quantum dynamics ⋮ Center-of-mass tomography and Wigner function for multimode photon states ⋮ NONLOCAL FIELD THEORY DRIVEN BY A DEFORMED PRODUCT: GENERALIZATION OF KALB–RAMOND DUALITY ⋮ Quantum Fourier transform and tomographic Rényi entropic inequalities ⋮ BASICS OF QUANTUM MECHANICS, GEOMETRIZATION AND SOME APPLICATIONS TO QUANTUM INFORMATION ⋮ Extended Voros product in the coherent states framework

This page was built for publication: Alternative commutation relations, star products and tomography