Entanglement properties of topological color codes

Understand

The entanglement properties of a class of topological stabilizer states, the so called \emph{topological color codes} defined on a two-dimensional lattice or \emph{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 the Kitaev's toric code.
• While a qubit is maximally entangled with rest of the system, two qubits are no longer entangled showing that the color code is genuinely multipartite entangled.