  We introduce the concept of quantum weight as a fundamental property of
quantum many-body systems that is encoded in the ground-state static structure
factor and characterizes density fluctuation at long wavelength. We show that
quantum weight of three-dimensional electron systems is related by a sum rule
to the inverse dielectric function, which describes electron energy loss
spectrum. Using this relation, we derive an upper and a lower bound on the
quantum weight of real materials in terms of their electron density, static
dielectric constant, and plasmon energy. For systems with short-range
interactions or Coulomb systems in reduced dimensions, we derive a sum rule
relating the quantum weight to the optical conductivity and establish a
remarkable connection with the quantum geometry of many-body ground states. Our
work highlights quantum weight as a key material parameter that can be
experimentally determined.
