  The bulk polarization is a $\mathbb{Z}_2$ topological invariant
characterizing non-interacting systems in one dimension with chiral or
particle-hole symmetries. We show that the bulk polarization can always be
determined from the single-particle entanglement spectrum, even in the absence
of symmetries that quantize it. In the symmetric case, the known relation
between the bulk polarization and the number of virtual topological edge modes
is recovered. We use the bulk polarization to compute Chern numbers in 1D and
2D, which illuminates their known relation to the entanglement spectrum.
Furthermore we discuss an alternative bulk polarization that can carry more
information about the surface spectrum than the conventional one and can
simplify the calculation of Chern numbers.
