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Entanglement Theory Quantum Correlations

Skein Theory and Topological Quantum Registers: Braiding Matrices and Topological Entanglement Entropy of Non-Abelian Quantum Hall States

arXiv
Authors: Kazuhiro Hikami

Year

2007

Paper ID

49069

Status

Preprint

Abstract Read

~2 min

Abstract Words

93

Citations

N/A

Abstract

We study topological properties of quasi-particle states in the non-Abelian quantum Hall states. We apply a skein-theoretic method to the Read--Rezayi state whose effective theory is the SU(2)_K Chern--Simons theory. As a generalization of the Pfaffian K=2 and the Fibonacci K=3 anyon states, we compute the braiding matrices of quasi-particle states with arbitrary spins. Furthermore we propose a method to compute the entanglement entropy skein-theoretically. We find that the entanglement entropy has a nontrivial contribution called the topological entanglement entropy which depends on the quantum dimension of non-Abelian quasi-particle intertwining two subsystems.

Why This Paper Matters

  • This paper contributes to the Entanglement Theory & Quantum Correlations research area in the Quantum Articles archive.
  • It adds a 2007 reference point for readers tracking recent quantum research.
  • We study topological properties of quasi-particle states in the non-Abelian quantum Hall states.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:0709.2409 [2] arXiv https://arxiv.org/abs/0709.2409 [3] Publisher https://arxiv.org/abs/0709.2409

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