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We present two efficient schemes which can simultaneously accomplishhyperentanglement concentration and purification for two-photon four-qubitsystems in an unknown partially hyperentangled mixed states. The first cancorrect errors in the polarization entanglement and extract maximalhyperentanglement in polarization and spatial mode with additional partialfrequency entanglement. The second uses additional maximal frequencyentanglement to purify and concentrate hyperentanglement in polarization andspatial mode deterministically. Both of the two schemes are only based onexisting optical devices and cross-Kerr nonlinearities.

Synchronous concentration and purification schemes of arbitrary unknown hyperentangled mixed states