Physical proof of the topological entanglement entropy inequality

Understand

Recently it was shown that the topological entanglement entropy (TEE) of a two-dimensional gapped ground state obeys the universal inequality $\gamma \geq \log \mathcal{D}$, where $\gamma$ is the TEE and $\mathcal{D}$ is the total quantum dimension of all anyon excitations, $\mathcal{D} = \sqrt{\sum_a d_a^2}$.

• Here we present an alternative, more direct proof of this inequality.
• Our proof uses only the strong subadditivity property of the von Neumann entropy together with a few physical assumptions about the ground state density operator.
• Our derivation naturally generalizes to a variety of systems, including spatially inhomogeneous systems with defects and boundaries, higher dimensional systems, and mixed states.