Physical proof of the topological entanglement entropy inequality

Recently it was shown that the topological entanglement entropy (TEE) of a two-dimensional gapped ground state obeys the universal inequality γgeq log mathcal{D}, where γ is the TEE and mathcal{D} is the total quantum dimension of all anyon excitations, mathcal{D} = sqrt{sum_a d_a²}. 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.