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Entanglement properties of topological color codes

Kargarian, M ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. DOI: 10.1103/PhysRevA.78.062312
  3. Publisher: 2008
  4. Abstract:
  5. The entanglement properties of a class of topological stabilizer states, the so-called topological color codes defined on a two-dimensional lattice or 2-colex, are calculated. The topological entropy is used to measure the entanglement of different bipartitions of the 2-colex. The dependency of the ground-state degeneracy on the genus of the surface shows that the color code can support a topological order, and the contribution of the color in its structure makes it interesting to compare with Kitaev's toric code. While a qubit is maximally entangled with the rest of the system, two qubits are no longer entangled showing that the color code is genuinely multipartite entangled. For a convex region, it is found that entanglement entropy depends only on the degrees of freedom living on the boundary of two subsystems. The boundary scaling of entropy is supplemented with a topological subleading term, which for a color code defined on a compact surface, is twice over the toric code. From the entanglement entropy we construct a set of bipartitions in which the diverging term arising from the boundary term is washed out, and the remaining nonvanishing term will have a topological nature. Besides the color code on the compact surface, we also analyze the entanglement properties of a version of color code with a border, i.e., triangular color code. © 2008 The American Physical Society
  6. Keywords:
  7. Color ; Color codes ; Entropy ; Optical properties ; Powders ; Topology ; Two dimensional ; Boundary terms ; Degrees of freedoms ; Entanglement entropies ; Entanglement properties ; Stabilizer states ; Sub systems ; Topological entropies ; Topological orders ; Toric codes ; Codes (symbols)
  8. Source: Physical Review A - Atomic, Molecular, and Optical Physics ; Volume 78, Issue 6 , 2008 ; 10502947 (ISSN)
  9. URL: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.78.062312