Entanglement negativity and topological order

Understand

We use the entanglement negativity, a measure of entanglement for mixed states, to probe the structure of entanglement in the ground state of a topologically ordered system.

• Through analytical calculations of the negativity in the ground state(s) of the toric code model, we explicitly show that the entanglement of a region $A$ and its complement $B$ is the sum of two types of contributions.
• The first type of contributions consists of \textit{boundary entanglement}, which we see to be insensitive to tracing out the interior of $A$ and $B$.
• It therefore entangles only degrees of freedom in $A$ and $B$ that are close to their common boundary.