(Abstract) We study the CP violation in the Higgs boson and toponia production process at the ILC
where the toponia are produced near the threshold. We analytically calculated the density matrix
for the production and decay of the toponia.
Then, based on it, we propose three completely independent CP observables, which come from the longitudinal-transverse interferences in the azimuthal angles of leptons, and the transverse-transverse interference in their sum. These three observables are well defined at the ILC, where the rest frame of the toponium can be reconstructed directly. Furthermore, the QCD-strong corrections, which are important near the threshold region, are also studied with the approximation of spin-independent QCD-Coulomb potential. While the total cross section is enhanced, the spin correlations predicted in this paper are not affected.