Entanglement from dissipation and holographic interpretation

Abstract

In this work we study a dissipative field theory where the dissipation process is manifestly related to dynamical entanglement and put it in the holographic context. Such endeavour is realized by further development of a canonical approach to study quantum dissipation, which consists of doubling the degrees of freedom of the original system by defining an auxiliary one. A time dependent entanglement entropy for the vacumm state is calculated and a geometrical interpretation of the auxiliary system and the entropy is given in the context of the AdS/CFT correspondence using the Ryu-Takayanagi formula. We show that the dissipative dynamics is controlled by the entanglement entropy and there are two distinct stages: in the early times the holographic interpretation requires some deviation from classical General Relativity; in the later times the quantum system is described as a wormhole, a solution of the Einstein's equations near to a maximally extended black hole with two asymptotically AdS boundaries. We focus our holographic analysis in this regime, and suggest a mechanism similar to teleportation protocol to exchange (quantum) information between the two CFTs on the boundaries (see Maldacena et al. in Fortschr Phys 65(5):1700034, arXiv:1704.05333 [hep-th], 2017.

Hyperbolic ring based formulation for thermo field dynamics, quantum dissipation, entanglement, and holography

“…Dynamical entanglement generated by dissipation has been studied within the context of the ADS/CFT correspondence [8]; since holographic correspondence relates geometrical quantities with information coming from quantum field theory, in this reference the Ryu-Takayanagi formulae for the area of a minimal surface in a holographic geometry, is used for studying the entanglement between the degrees of freedom of dissipative conformal field theories; the holographic correspondence suggests then a teleportation protocol that interchange quantum information between the two conformal field theories on the boundaries of the dual geometry; such a protocol is similar to the mechanism that makes a wormhole traversable [9,10].…”

The gravity dual of real-time CFT at finite temperature

“…Generalizations of our geometry that include charge and angular momentum would also be of interest. Another line of future research would be deforming the TFD (decoupled) field theory Hamiltonian H R − H L , with a local coupling term ∼ g O R O L leading to a traversable wormhole [37,38,39,40,33].…”

Modular Hamiltonian for holographic excited states

“…where the coordinate y ≡ ðχ; Ω d−2 Þ involves a noncompact component χ, while Ω d−2 describes a (d − 2)-sphere. The holographic coordinate u can be extended to take all the real values (e.g., [60]); thus u > 0 stands for the wedge that, after a suitable change of coordinates: u 2 → u 2 − 1, is dual to the a hyperbolic cylinder on the boundary [57], that can be conformally mapped to a ball shaped region, or to one of the two wedges of the flat Rindler spacetime [9]. Figure 4 illustrates how the Killing vector ζ ≡ ∂ t , asymptotically coincides (up to a conformal map) with the vector ∂ t of the boundary metric (3.2).…”

“…Different formulations of the thermal state condition as a constraint in the string context can be found in[60,62].…”