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

TL;DR

This paper introduces a new quasi-probability distribution for spin-1/2 particles that visually represents complex quantum states and can handle multiple angular momentum shells simultaneously.

Contribution

It presents a novel Wigner-like function for qubits that improves visualization and representation of diverse quantum states, including superpositions and mixtures.

Findings

Provides a clear graphical representation of various quantum states.

Capable of representing multiple angular momentum shells simultaneously.

Enhances understanding of spin ensemble states.

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.