Abstract
In this work we study the nature of correlations among mixed states in the setup of two symmetric strips. We use various tools to determine how the bulk geometry could be reconstructed from the boundary mixed information. These tools would be the modular Hamiltonian and modular flow, OPE blocks, quantum recovery channels such as Petz map, Uhlmann holonomy and Wilson lines. We comment on the similarities and connections between these approaches in our symmetric setup of a mixed system. Specially, we use parameters such as dissipation which is being modeled by the mass of graviton, and also the same sign charge of the two strips to find connections between these different approaches. Then, using Uhlmann fidelity as the correlation measure, we look into the various types of correlations in mixed systems such as discord. Next, we use simple results of modular Hamiltonian for fermions to get insights about the relations between modular flow and entanglement and complexity of purification (EoP/CoP), and also behavior of modular flows in confining geometries. Finally, we study the dynamics of correlations using various information speeds and also model of void formation in CFTs and again we comment on their relationships with the behavior of EoP and CoP.
Highlights
In the setup of holography, out of information and entanglement in the boundary field theory side, the one dimension higher bulk geometry could be reconstructed
We study the dynamics of correlations using various information speeds and model of void formation in conformal field theory (CFT) and again we comment on their relationships with the behavior of entanglement of purification (EoP) and complexity of purification (CoP)
We used the results for EoP and CoP of charged and massive gravity backgrounds and compared various results with each other
Summary
In the setup of holography, out of information and entanglement in the boundary field theory side, the one dimension higher bulk geometry could be reconstructed. In [11], some specific connections between universal recovery channels and modular Hamiltonian have been mentioned as they could show that by perturbing a bulk state in a direction of a bulk operator which is within a boundary subregion causal wedge, the modular Hamiltonian of the boundary would correspondingly respond This would be related to the noncommutative version of Bayes rule which could be used to reconstruct the lost information similar to a quantum error correction system. As Berry curvature of modular Hamiltonians could sew together the orthonormal coordinate systems along the Hubeny, Rangamani, Ryu, Takayanagi (HRRT) surfaces and lead to the bulk reconstruction, [7], we would like to examine how this proposal would work for the case of two disconnected versus connected subsystems and investigate the properties of the modular Hamiltonian and modular flows during the phase transitions
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