Wigner tomography of multispin quantum states

TL;DR

This paper presents a method for visualizing multispin quantum states using Wigner representations, enabling complete characterization through expectation measurements, demonstrated with NMR experiments on up to three spins.

Contribution

The authors develop a general methodology for experimentally reconstructing multispin Wigner functions via expectation values of spherical tensor operators.

Findings

Successful experimental demonstration with up to three spins

Complete visualization of quantum states using Wigner shapes

Method applicable to finite-dimensional multispin systems

Abstract

We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations of spherical harmonics [A. Garon, R. Zeier, and S. J. Glaser, Phys. Rev. A 91, 042122 (2015)]. We develop a general methodology to experimentally recover these shapes by measuring expectation values of rotated axial spherical tensor operators and provide an interpretation in terms of fictitious multipole potentials. Our approach is experimentally demonstrated for quantum systems consisting of up to three spins using nuclear magnetic resonance spectroscopy.