  In this study, we discuss a new type of bulk-boundary correspondence which
holds for topological insulators and superconductors when the parity-time
($PT$) and/or parity-particle-hole ($PC$) symmetry are present. In these
systems, even when the bulk topology is nontrivial, the edge spectrum is
generally gapped, and thus the conventional bulk-boundary correspondence does
not hold. We find that, instead of the edge spectrum, the single-particle
entanglement spectrum becomes gapless when the bulk topology is nontrivial:
i.e., the $\textit{bulk-entanglement}$ $\textit{spectrum}$
$\textit{correspondence}$ holds in $PT$- and/or $PC$-symmetric topological
insulators and superconductors. After showing the correspondence using
$K$-theoretic approach, we provide concrete models for each symmetry class up
to three dimensions where nontrivial topology due to $PT$ and/or $PC$ is
expected. An implication of our results is that, when the bulk topology under
$PT$ and/or $PC$ symmetry is nontrivial, the non-interacting many-body
entanglement spectrum is multiply degenerate in one dimension and is gapless in
two or higher dimensions.
