  Multipolar magnetism is an emerging field of quantum materials research. The
building blocks of multipolar phenomena are magnetic ions with a non-Kramers
doublet, where the orbital and spin degrees of freedom are inextricably
intertwined, leading to unusual spin-orbital entangled states. The detection of
such subtle forms of matter has, however, been difficult due to a limited
number of appropriate experimental tools. In this work, motivated by a recent
magnetostriction experiment on Pr$_2$Zr$_2$O$_7$, we theoretically investigate
how multipolar quantum spin ice, an elusive three dimensional quantum spin
liquid, and other multipolar ordered phases in the pyrochlore materials can be
detected using magnetostriction. We provide theoretical results based on
classical and/or quantum studies of non-Kramers and Kramers magnetic ions, and
contrast the behaviors of distinct phases in both systems. Our work paves an
important avenue for future identification of exotic ground states in
multipolar systems.
