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Bit Threads and Holographic Entanglement

Freedman, Michael ; Headrick, Matthew

Communications in mathematical physics, 2017-05, Vol.352 (1), p.407-438 [Periódico revisado por pares]

Berlin/Heidelberg: Springer Berlin Heidelberg

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  • Título:
    Bit Threads and Holographic Entanglement
  • Autor: Freedman, Michael ; Headrick, Matthew
  • Assuntos: Classical and Quantum Gravitation ; Complex Systems ; Entanglement ; Entropy ; Equivalence ; Information theory ; Mathematical and Computational Physics ; Mathematical Physics ; Minimal surfaces ; Physics ; Physics and Astronomy ; Quantum Physics ; Relativity Theory ; Riemann manifold ; Theorems ; Theoretical
  • É parte de: Communications in mathematical physics, 2017-05, Vol.352 (1), p.407-438
  • Descrição: The Ryu-Takayanagi (RT) formula relates the entanglement entropy of a region in a holographic theory to the area of a corresponding bulk minimal surface. Using the max flow-min cut principle, a theorem from network theory, we rewrite the RT formula in a way that does not make reference to the minimal surface. Instead, we invoke the notion of a “flow”, defined as a divergenceless norm-bounded vector field, or equivalently a set of Planck-thickness “bit threads”. The entanglement entropy of a boundary region is given by the maximum flux out of it of any flow, or equivalently the maximum number of bit threads that can emanate from it. The threads thus represent entanglement between points on the boundary, and naturally implement the holographic principle. As we explain, this new picture clarifies several conceptual puzzles surrounding the RT formula. We give flow-based proofs of strong subadditivity and related properties; unlike the ones based on minimal surfaces, these proofs correspond in a transparent manner to the properties’ information-theoretic meanings. We also briefly discuss certain technical advantages that the flows offer over minimal surfaces. In a mathematical appendix, we review the max flow-min cut theorem on networks and on Riemannian manifolds, and prove in the network case that the set of max flows varies Lipshitz continuously in the network parameters.
  • Editor: Berlin/Heidelberg: Springer Berlin Heidelberg
  • Idioma: Inglês
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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