  We present two efficient schemes which can simultaneously accomplish
hyperentanglement concentration and purification for two-photon four-qubit
systems in an unknown partially hyperentangled mixed states. The first can
correct errors in the polarization entanglement and extract maximal
hyperentanglement in polarization and spatial mode with additional partial
frequency entanglement. The second uses additional maximal frequency
entanglement to purify and concentrate hyperentanglement in polarization and
spatial mode deterministically. Both of the two schemes are only based on
existing optical devices and cross-Kerr nonlinearities.
