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From topological to quantum entanglement

  • D. MelnikovEmail author
  • A. Mironov
  • S. Mironov
  • A. Morozov
  • An. Morozov
Open Access
Regular Article - Theoretical Physics

Abstract

Entanglement is a special feature of the quantum world that reflects the existence of subtle, often non-local, correlations between local degrees of freedom. In topological theories such non-local correlations can be given a very intuitive interpretation: quantum entanglement of subsystems means that there are “strings” connecting them. More generally, an entangled state, or similarly, the density matrix of a mixed state, can be represented by cobordisms of topological spaces. Using a formal mathematical definition of TQFT we construct basic examples of entangled states and compute their von Neumann entropy.

Keywords

Topological Field Theories Chern-Simons Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • D. Melnikov
    • 1
    • 2
    Email author
  • A. Mironov
    • 2
    • 3
    • 4
  • S. Mironov
    • 2
    • 5
    • 6
    • 7
  • A. Morozov
    • 2
    • 4
  • An. Morozov
    • 2
    • 4
    • 6
  1. 1.International Institute of PhysicsFederal University of Rio Grande do NorteNatalBrazil
  2. 2.Institute for Theoretical and Experimental PhysicsMoscowRussia
  3. 3.I.E. Tamm Theory DepartmentLebedev Physics InstituteMoscowRussia
  4. 4.Institute for Information Transmission ProblemsMoscowRussia
  5. 5.Institute for Nuclear Research of the Russian Academy of SciencesMoscowRussia
  6. 6.Moscow Institute of Physics and TechnologyDolgoprudnyRussia
  7. 7.Institute for Theoretical and Mathematical PhysicsMoscowRussia

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