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Topological entanglement entropy.

Alexei Kitaev1, John Preskill

  • 1Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125, USA.

Physical Review Letters
|April 12, 2006
PubMed
Summary
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We present a universal method to characterize quantum entanglement in 2D topological media. This reveals a universal constant, -gamma, that captures global entanglement features in the ground state.

Area of Science:

  • Condensed Matter Physics
  • Quantum Information Theory
  • Topological Quantum Field Theory

Background:

  • Topologically ordered media exhibit unique quantum entanglement properties in their ground states.
  • Characterizing many-particle quantum entanglement is crucial for understanding complex quantum systems.

Purpose of the Study:

  • To formulate a universal characterization of quantum entanglement in the ground state of 2D topologically ordered media.
  • To identify universal constants that describe global entanglement features.

Main Methods:

  • Consideration of a disk in a 2D medium with a smooth boundary of length L.
  • Derivation of the marginal density operator rho for interior degrees of freedom by tracing out exterior variables.
  • Utilizing topological quantum field theory (TQFT) methods to derive a formula for the entanglement entropy constant.

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Main Results:

  • The von Neumann entropy S(rho) of the traced-out system exhibits a universal form S(rho) = alphaL - gamma + ..., where terms vanish as L approaches infinity.
  • Identification of -gamma as a universal constant characterizing global entanglement features.
  • Derivation of a formula for gamma based on the superselection sectors of the medium.

Conclusions:

  • The study provides a universal characterization of many-particle quantum entanglement in gapped 2D topological phases.
  • -gamma offers a new, universal measure of entanglement in these systems.
  • TQFT methods are effective for understanding topological entanglement properties.