Wigner process tomography: Visualization of spin propagators and their spinor properties

TL;DR

This paper introduces a method to visualize and experimentally reconstruct spin propagators using Wigner representations, revealing their spinor properties through nuclear magnetic resonance techniques.

Contribution

It presents a novel tomography approach for spin propagators in Wigner representation, enabling direct visualization of their spinor characteristics.

Findings

Successful experimental reconstruction of quantum gates via NMR.

Visualization of spinor properties of spin-1/2 propagators.

Method applicable to finite-dimensional quantum systems.

Abstract

We study the tomography of propagators for spin systems in the context of finite-dimensional Wigner representations, which completely characterize and visualize operators using shapes assembled from linear combinations of spherical harmonics. The Wigner representation of a propagator can be experimentally recovered by measuring expectation values of rotated axial spherical tensor operators in an augmented system with an additional ancilla qubit. The methodology is experimentally demonstrated for standard one-qubit quantum gates using nuclear magnetic resonance spectroscopy. In particular, this approach provides a direct and compelling visualization of the spinor property of the propagators corresponding to the rotation of a spin 1/2 particle.