State-dependent divergences in the entanglement entropy

We show the entanglement entropy in certain quantum field theories to contain state-dependent divergences. Both perturbative and holographic examples are exhibited. However, quantities such as the relative entropy and the generalized entropy of black holes remain finite, due to cancellation of divergences. We classify all possible state-dependent divergences that can appear in both perturbatively renormalizeable and holographic covariant $d\le 6$ quantum field theories