Entanglement and complexity of purification in ( 1 + 1 )-dimensional free conformal field theories
H. A. Camargo,H. A. Camargo,Lucas Hackl,Michal P. Heller,Alexander Jahn,Tadashi Takayanagi,Tadashi Takayanagi,Bennet Windt +7 more
- Vol. 3, Iss: 1, pp 013248
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In this paper, the massless limit of the free bosonic theory and the corresponding behavior of the mutual information were analyzed for two intervals in the vacuum of the Ising conformal field theory.Abstract:
Finding pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace is necessarily a challenging task. Nevertheless, such purifications play the key role in characterizing quantum information-theoretic properties of mixed states via entanglement and complexity of purifications. In this article, we analyze these quantities for two intervals in the vacuum of free bosonic and Ising conformal field theories using the most general Gaussian purifications. We provide a comprehensive comparison with existing results and identify universal properties. We further discuss important subtleties in our setup: the massless limit of the free bosonic theory and the corresponding behavior of the mutual information, as well as the Hilbert space structure under the Jordan-Wigner mapping in the spin chain model of the Ising conformal field theory.read more
Citations
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Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model
Aranya Bhattacharya,Aranya Bhattacharya,Arpan Bhattacharyya,Pratik Nandy,Ayan K. Patra,Ayan K. Patra +5 more
TL;DR: In this paper, the authors study the entanglement islands and subsystem volume complexity corresponding to the left/right entanglements of a conformal defect in d-dimensions in a Randall-Sundrum (RS) braneworld model with subcritical tension brane.
Journal ArticleDOI
Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model
TL;DR: In this paper, the authors study the entanglement islands and subsystem volume complexity corresponding to the left/right entanglements of a conformal defect in $d$-dimensions in the Randall-Sundrum (RS) braneworld model with subcritical tension brane.
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Path integral optimization from Hartle-Hawking wave function
TL;DR: Caputa et al. as discussed by the authors proposed a gravity dual description of the path integral optimization in conformal field theories using Hartle-Hawking wave functions in anti-de Sitter spacetime.
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Holographic path-integral optimization
TL;DR: In this paper, it was shown that the Hartle-Hawking wave function is equivalent to the path-integral optimization procedure in CFT and that the metrics that maximize gravity wave functions computed in particular holographic geometries, precisely match those derived in the pathintegral optimisation procedure for their dual CFT states.
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Bosonic and fermionic Gaussian states from K\"ahler structures
Lucas Hackl,Eugenio Bianchi +1 more
TL;DR: In this paper, it was shown that fermionic and bosonic Gaussian states can be uniquely characterized by their linear complex structure, which is a linear map on the classical phase space.
References
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Holographic Derivation of Entanglement Entropy from the anti de Sitter Space/Conformal Field Theory Correspondence
Shinsei Ryu,Tadashi Takayanagi +1 more
TL;DR: It is argued that the entanglement entropy in d + 1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS(d+2), analogous to the Bekenstein-Hawking formula for black hole entropy.
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Guifre Vidal,Reinhard F. Werner +1 more
TL;DR: A measure of entanglement that can be computed effectively for any mixed state of an arbitrary bipartite system is presented and it is shown that it does not increase under local manipulations of the system.
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Conformal Field Theory
TL;DR: This paper developed conformal field theory from first principles and provided a self-contained, pedagogical, and exhaustive treatment, including a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algesas.
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Entanglement entropy and quantum field theory
Pasquale Calabrese,John Cardy +1 more
TL;DR: In this article, a systematic study of entanglement entropy in relativistic quantum field theory is carried out, where the von Neumann entropy is defined as the reduced density matrix ρA of a subsystem A of a 1+1-dimensional critical system, whose continuum limit is a conformal field theory with central charge c, and the results are verified for a free massive field theory.
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A covariant holographic entanglement entropy proposal
TL;DR: In this paper, a covariant generalization of the holographic entanglement entropy proposal of hep-th/0603001 is proposed to understand the time-dependence of entropy in generic quantum field theories.