  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.
