Holographic study of entanglement and complexity for mixed states

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. For entanglement, we 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 $\theta$. On the other hand, in order to probe the mixed state complexity we compute the mutual complexity ($\Delta C$) for the BTZ black hole and the hyperscaling violating geometry by incorporating the holographic subregion complexity conjecture. Furthermore, various aspects of holographic entanglement entropy such as entanglement Smarr relation and Fisher information metric has also been studied.