Abstract
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.
Highlights
The gauge/gravity duality [1,2,3] has been employed to holographically compute quantum information theoretic quantities and has thereby helped us to understand the bulk-boundary relations
In order to probe the mixed state complexity we compute the mutual complexity for the Banados Teitelboim Zanelli (BTZ) black hole and the hyperscaling violating geometry by incorporating the holographic subregion complexity conjecture
Among various observables of quantum information theory, entanglement entropy (EE) has been the most fundamental thing to study as it measures the correlation between two subsystems for a pure state
Summary
The gauge/gravity duality [1,2,3] has been employed to holographically compute quantum information theoretic quantities and has thereby helped us to understand the bulk-boundary relations. Preparing a mixed state on some Hilbert space H, starting from a reference (pure) state involves the extension of the Hilbert space H by introducing auxiliary degrees of freedom [48,50] In this setup, a quantity denoted as the mutual complexity ΔC has been prescribed in order to probe the concept of purification complexity [47,48,49,50]. The other setup, we consider that the boundary Cauchy slice σ is a collection of two adjacent subsystems A and B of width l with A ∩ B 1⁄4 0 (zero overlap) and Ac 1⁄4 B In this setup we compute the mutual complexity between a subregion A and the full system A ∪ Ac. The paper is organized as follows.
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