  We study entanglement spectra of gapped states on the surfaces of
symmetry-protected topological phases. These surface states carry anomalies
that do not allow them to be terminated by a trivial state. Their entanglement
spectra are dominated by non-universal features, which reflect the underlying
bulk. We introduce a modified type of entanglement spectra that incorporate the
anomaly and argue that they correspond to physical edge states between
different surface states. We support these arguments by explicit analytical and
numerical calculations for free and interacting surfaces of three-dimensional
topological insulators of electrons.
