CPV in $$e^{\mathbf{+}}$$ $$e^{\mathbf{-}}$$ H at 1 TeV ILC

CP violation is one of Sakharov’s conditions for the matter-antimatter asymmetry of the Universe. The experimentally observed size of CP violation is insufficient to account for this. Is CP violated in the Higgs sector? Could the SM-like Higgs boson be a mixture of CP even and CP odd states of an extended Higgs sector? With what precision could such effects be measured at future electron-positron colliders? These questions will be discussed in the light of the latest studies at ILC.