  Albeit occurring at zero temperature, quantum critical phenomena are known to
have a huge impact on the finite-temperature phase diagram of strongly
correlated systems -- an aspect which gives experimental access to their
observation. In particular the existence of a gapless, zero-temperature quantum
critical point is known theoretically to induce the existence of an extended
region in parameter space -- the so-called quantum critical fan --
characterized by power-law temperature dependences of all observables, with
exponents related to those of the quantum critical point. Identifying
experimentally the quantum critical fan and its crossovers to the other regions
(renormalized classical, quantum disordered) remains nonetheless a big
challenge. Focusing on paradigmatic models of quantum phase transitions, here
we show that quantum correlations - captured by the quantum variance of the
order parameter (I. Fr\'erot and T. Roscilde, Phys. Rev. B {\bf 94}, 075121
(2016)) - exhibit the temperature scaling associated with the quantum critical
regime over an extended parameter region, much broader than that revealed by
ordinary correlations, and with well-defined crossovers to the other regimes.
The link existing between the quantum variance and the dynamical
order-parameter susceptibility paves the way to an experimental reconstruction
of the quantum critical fan using \emph{e.g.} spectroscopy on strongly
correlated quantum matter.
