  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.
