  In this paper, we holographically quantify the entanglement and complexity
for mixed states by following the prescription of purification. The bulk theory
we consider in this work is a hyperscaling violating solution, characterized by
two parameters, hyperscaling violating exponent $\theta$ and dynamical exponent
$z$. This geometry is dual to a non-relativistic strongly coupled theory with
hidden Fermi surfaces. We first compute the holographic analogy of entanglement
of purification (EoP), denoted as the minimal area of the entanglement wedge
cross section and observe the effects of $z$ and $\theta$. Then in order to
probe the mixed state complexity we compute the mutual complexity for the BTZ
black hole and the hyperscaling violating geometry by incorporating the
holographic subregion complexity conjecture. We carry this out for two disjoint
subsystems separated by a distance and also when the subsystems are adjacent
with subsystems making up the full system. Furthermore, various aspects of
holographic entanglement entropy such as entanglement Smarr relation, Fisher
information metric and the butterfly velocity has also been discussed.
