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Fast Quantum Fourier-Heisenberg-Weyl Transforms

Valery Labunets, E. Rundblad, Jaakko T. Astola

We study the Fourier harmonic analysis of functions on discrete Heisenberg-Weyl groups and develop fast quantum Fourier-Heisenberg-Weyl transforms on these groups.

Birkhäuser Boston eBooksJan 1, 20021 citation

A study on Heisenberg-Weyl linear maps

Patra, Saikat, Bihalan Bhattacharya

Heisenberg-Weyl operators provide a Hermitian generalization of Pauli operators in higher dimensions. Positive maps arising from Heisenberg-Weyl operators have been studied along with several algebraic and spectral properties of Heisenberg-Weyl observables. This allows to generalize the study of Pauli type maps in higher dimesional algebra of operators.

arXiv:2506.05097Jun 5, 20250 citations

Heisenberg Group and Weyl Operators

Birkhäuser Basel eBooksJan 1, 20060 citations

Weyl calculus on the Fock space and Stratonovich-Weyl correspondence for Heisenberg motion groups

Benjamin Cahen

We construct a Stratonovich-Weyl correspondence for each generic representation of a Heisenberg motion group by using the Weyl calculus on the Fock space.

arXiv:2012.14398Dec 28, 20202 citations

On Non-Commutative Operator Graphs Generated by Reducible Unitary Representation of the Heisenberg-Weyl Group

Grigori Gennadievich Amosov, Мокеев Александр Сергеевич

arXiv:1812.02515International Journal of Theoretical PhysicsNov 28, 20188 citations

Operator algebras for general one-dimensional quantum mechanical potentials with discrete spectrum

Alfred W nsche

We define general lowering and raising operators of the eigenstates for one-dimensional quantum mechanical potential problems leading to discrete energy spectra and investigate their associative algebra. The Hamilton operator is quadratic in these lowering and raising operators and corresponding representations of operators for action and angle are found. The normally ordered representation of general operators using combinatorial elements such as partitions is derived. The introduction of generalized coherent states is discussed. Linear laws for the spacing of the energy eigenvalues lead to the Heisenberg–Weyl group and general quadratic laws of level spacing to unitary irreducible representations of the Lie group SU (1, 1) that is considered in detail together with a limiting transition from this group to the Heisenberg–Weyl group. The relation of the approach to quantum deformations is discussed. In two appendices, the classical and quantum mechanical treatment of the squared tangent potential is presented as a special case of a system with quadratic level spacing.We define general lowering and raising operators of the eigenstates for one-dimensional quantum mechanical potential problems leading to discrete energy spectra and investigate their associative algebra. The Hamilton operator is quadratic in these lowering and raising operators and corresponding representations of operators for action and angle are found. The normally ordered representation of general operators using combinatorial elements such as partitions is derived. The introduction of generalized coherent states is discussed. Linear laws for the spacing of the energy eigenvalues lead to the Heisenberg–Weyl group and general quadratic laws of level spacing to unitary irreducible representations of the Lie group SU (1, 1) that is considered in detail together with a limiting transition from this group to the Heisenberg–Weyl group. The relation of the approach to quantum deformations is discussed. In two appendices, the classical and quantum mechanical treatment of the squared tangent potential is presented as a special case of a system with quadratic level spacing.

Journal of Optics B Quantum and Semiclassical OpticsSep 20, 200212 citations

The Weyl-Heisenberg Group

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The Weyl-Heisenberg Group

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