Towards a complete, continuous, Wigner function for an ensemble of spins or qubits

Abstract

We present a new quasi-probability distribution function for ensembles of spin-half particles or qubits that has many properties in common with Wigner's original function for systems of continuous variables. We show that this function provides clear and intuitive graphical representation of a wide variety of states, including Fock states, spin-coherent states, squeezed states, superpositions and statistical mixtures. Unlike previous attempts to represent ensembles of spins/qubits, this distribution is capable of simultaneously representing several angular momentum shells.

11 pages, 6 figures. If viewed in adobe reader all figures except Fig 2 are interactive. For the non-interactive figures corresponding to those of the published version of this work please see version one of this preprint (which is also a much smaller file)

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• Analysis of continuous and discrete Wigner approximations for spin dynamics
• Continuous phase spaces and the time evolution of spins: star products and spin-weighted spherical harmonics
• Measurement of complete and continuous Wigner functions for discrete atomic systems
• Time evolution of coupled spin systems in a generalized Wigner representation
• Symmetry-adapted decomposition of tensor operators and the visualization of coupled spin systems
• Geometric representation of spin correlations and applications to ultracold systems
• Hermite Polynomial Representation of the Spin States