  We propose the entanglement dipole polarization to describe the topological
quadrupole phase. The quadrupole moment can be regarded as a pair of the dipole
moment, in which the total dipole moment is canceled. The entanglement
polarization, we propose, is useful to detect such a constituent dipole
polarization. We first introduce partitions of sites in the unit cell and
divide the system into two subsystems. Then, introducing an entanglement
Hamiltonian by tracing out one of the subsystems partly, we compute the dipole
polarization of the occupied states associated with the entanglement
Hamiltonian, which is referred to as the entanglement polarization. Although
the total dipole polarization is vanishing, those of the subsystems can be
finite. The entanglement dipole polarization is quantized by reflection
symmetries. We also introduce the entanglement polarization of the edge states,
which reveals that the edge states themselves are gapped and topologically
nontrivial. Therefore, such edge states yield the zero energy edge states if
the system has boundaries. This is the origin of the corner states.
