  Operating quantum sensors and quantum computers would make data in the form
of quantum states available for purely quantum processing, opening new avenues
for studying physical processes and certifying quantum technologies. In this
Perspective, we review a line of works dealing with measurements that reveal
structural properties of quantum datasets given in the form of product states.
These algorithms are universal, meaning that their performances do not depend
on the reference frame in which the dataset is provided. Requiring the
universality property implies a characterization of optimal measurements via
group representation theory.
