  The holographic dark energy models provide an alternative description of the
dark energy. These models are motivated by the possible application of
holographic principle to the dark energy problem. We study the one parameter Li
holographic dark energy and the two parameter Barrow holographic dark energy
models using configuration entropy of the matter distribution in the Universe.
The configuration entropy rate exhibits a distinct minimum at a specific scale
factor that corresponds to the epoch, beyond which the dark energy takes a
driving role in the accelerated expansion of the Universe. We find that the
location of the minimum and magnitude of the entropy rate at the minimum are
sensitive to the parameters of the models. We find the best fit relations
between these quantities and the parameters of each model. We propose that
these relations can be used to constrain the parameters of the holographic dark
energy models from the future measurements of the configuration entropy at
multiple redshifts. Further, the Barrow holographic dark energy model is based
on Barrow entropy which modifies the standard Bekenstein-Hawking entropy, to
capture the deformation of the black-hole surface due to quantum gravitational
effects. We find that the location and amplitude of the minimum of the
configuration entropy rate is strongly sensitive to the deformation exponent
$\Delta$ in the Barrow model. Our study suggests that signatures of the quantum
gravitational effects on the future event horizon may be detected from the
study of the configuration entropy of the matter distribution on large-scales.
