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arXiv:1904.13090

Holographic complexity of boosted black brane and Fisher information

Sourav Karar, Rohit Mishra, Sunandan Gangopadhyay

Published Apr 30, 2019• 6 citations
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Abstract

In this paper, we have studied the holographic subregion complexity for boosted black brane for strip like subsystem. The holographic subregion complexity has been computed for a subsystem chosen along and perpendicular to the boost direction. We have observed that there is an asymmetry in the result due to the boost parameter which can be attributed to the asymmetry in the holographic entanglement entropy. The Fisher information metric and the fidelity susceptibility have also been computed using bulk dual prescriptions. It is observed that the two metrics computed holographically are not related for both the pure black brane as well as the boosted black brane. This is one of the main findings in this paper and the holographic results have been compared with the results available in the quantum information literature where it is known that the two distances are related to each other in general.

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In this paper, we have studied the holographic subregion complexity for boosted black brane for strip like subsystem. The holographic subregion complexity has been computed for a subsystem chosen along and perpendicular to the boost direction. We have observed that there is an asymmetry in the result due to the boost parameter which can be attributed to the asymmetry in the holographic entanglement entropy. The Fisher information metric and the fidelity susceptibility have also been computed using bulk dual prescriptions. It is observed that the two metrics computed holographically are not related for both the pure black brane as well as the boosted black brane. This is one of the main findings in this paper and the holographic results have been compared with the results available in the quantum information literature where it is known that the two distances are related to each other in general.
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 $\ensuremath{\theta}$ and dynamical exponent zzz. This geometry is due to a nonrelativistic strongly coupled theory with hidden Fermi surfaces. We first compute the holographic analogy of entanglement of purification, denoted as the minimal area of the entanglement wedge cross section and observe the effects of zzz and $\ensuremath{\theta}$. Then 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. 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 the entanglement Smarr relation, the Fisher information metric, and the butterfly velocity have also been discussed.
We study the effects of asymmetry in the entanglement thermodynamics of CFT subsystems. It is found that “boosted” Dp-brane backgrounds give rise to the first law of the entanglement thermodynamics where the CFT pressure asymmetry plays a decisive role in the entanglement. Two different strip like subsystems, one parallel to the boost and the other perpendicular, are studied in the perturbative regime [Formula: see text]. We mainly seek to quantify this entanglement asymmetry as a ratio of the first-order entanglement entropies of the excitations. We discuss the AdS-wave backgrounds at zero temperature having maximum asymmetry from where a bound on entanglement asymmetry is obtained. The entanglement asymmetry reduces as we switch on finite temperature in the CFT while it is maximum at zero temperature.
Abstract In the context of relating AdS/CFT to quantum information theory, we propose a holographic dual of Fisher information metric for mixed states in the boundary field theory. This amounts to a holographic measure for the distance between two mixed quantum states. For a spherical subregion in the boundary we show that this is related to a particularly regularized volume enclosed by the Ryu-Takayanagi surface. We further argue that the quantum correction to the proposed Fisher information metric is related to the quantum correction to the boundary entanglement entropy. We discuss consequences of this connection.
Abstract We study the behaviour of holographic entanglement entropy (HEE) in near equilibrium thermal states which are macroscopically described by conformal relativistic hydrodynamic flows dual to dynamical black brane geometries. We compute HEE for strip-shaped subsystems in boundary dimensions d = 2, 3, 4, which provides us with general qualitative inferences on the interplay between fluid flows and entanglement dynamics. At first, we consider the zeroth order in hydrodynamic derivative expansion, holographically described by stationary boosted black branes. Working non-perturbatively in fluid velocity, we find that, as the fluid velocity approaches its relativistic upper limit, the UV regulated HEE exhibits a divergence at arbitrary temperature. Also, the holographic mutual information between two relatively close subsystems vanishes at some critical fluid velocity and remains zero beyond it. We then compute HEE in an excited state of the fluid in the presence of the sound mode. As a simplified setup, we first work with non-dissipative dynamics in d = 2, where the time evolution of HEE is studied in the presence of the sound mode and a propagating pressure pulse. In d = 4, working upto first order in derivative expansion, we find that dissipative sound modes produce an additional dynamical UV divergence which is subleading compared to the ‘area law divergence’. No such divergence is observed for dissipative sound mode in d = 3.
In the context of relating AdS/CFT to quantum information theory, we propose a holographic dual of Fisher information metric for mixed states in the boundary field theory. This amounts to a holographic measure for the distance between two mixed quantum states. For a spherical subregion in the boundary we show that this is related to a particularly regularized volume enclosed by the Ryu-Takayanagi surface. We further argue that the quantum correction to the proposed Fisher information metric is related to the quantum correction to the boundary entanglement entropy. We discuss consequences of this connection.
In the context of relating AdS/CFT to quantum information theory, we propose a holographic dual of Fisher information metric for mixed states in the boundary field theory. This amounts to a holographic measure for the distance between two mixed quantum states. For a spherical subregion in the boundary we show that this is related to a particularly regularized volume enclosed by the Ryu-Takayanagi surface. We further argue that the quantum correction to the proposed Fisher information metric is related to the quantum correction to the boundary entanglement entropy. We discuss consequences of this connection.