Symmetry-adapted decomposition of tensor operators and the visualization of coupled spin systems
arXiv:1809.09006 · doi:10.1088/1751-8121/ab93ff
Abstract
We study the representation and visualization of finite-dimensional quantum systems. In a generalized Wigner representation, multi-spin operators can be decomposed into a symmetry-adapted tensor basis and they are mapped to multiple spherical plots that are each assembled from linear combinations of spherical harmonics. We apply two different approaches based on explicit projection operators and coefficients of fractional parentage in order to obtain this basis for up to six spins 1/2 (qubits), for which various examples are presented. An extension to two coupled spins with arbitrary spin numbers (qudits) is provided, also highlighting a quantum system of a spin 1/2 coupled to a spin 1 (qutrit).
arXiv comment29 pages
References in corpus (25)
- Three qubits can be entangled in two inequivalent ways
- Persistent entanglement in arrays of interacting particles
- Training Schrödinger's cat: quantum optimal control
- The European Quantum Technologies Roadmap
- Four qubits can be entangled in nine different ways
- Discrete phase space based on finite fields
- Characterizing the entanglement of symmetric many-particle spin-1/2 systems
- Phase-space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries
- Quantum computers in phase space
- Wigner Functions for Arbitrary Quantum Systems
- Framed Hilbert space: hanging the quasi-probability pictures of quantum theory
- A General Theory of Phase-Space Quasiprobability Distributions
- Quantum phase space measurement and entanglement validation made easy
- Visualizing operators of coupled spin systems
- Discrete Moyal-type Representations for a Spin
- Continuous phase-space representations for finite-dimensional quantum states and their tomography
- A general approach to quantum mechanics as a statistical theory
- Wigner tomography of multispin quantum states
- Wigner process tomography: Visualization of spin propagators and their spinor properties
- Compact Hermitian Young Projection Operators
- Hermitian Young Operators
- Transition Operators
- Continuous phase spaces and the time evolution of spins: star products and spin-weighted spherical harmonics
- Time evolution of coupled spin systems in a generalized Wigner representation
- Towards a complete, continuous, Wigner function for an ensemble of spins or qubits
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