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Hyperentanglement, defined as the entanglement in several degrees of freedom(DOFs) of a quantum system, has attracted much attention recently. Here weinvestigate the possibility of concentrating the two-photon four-qubit systemsin partially hyperentangled states in both the spatial mode and thepolarization DOFs with linear optics. We first introduce ourparameter-splitting method to concentrate the systems in the partiallyhyperentangled states with known parameters, including partially hyperentangledBell states and cluster states. Subsequently, we present another two nonlocalhyperentanglement concentration protocols (hyper-ECPs) for the systems inpartially hyperentangled unknown states, resorting to the Schmidt projectionmethod. It will be shown that our parameter-splitting method is very efficientfor the concentration of the quantum systems in partially entangled states withknown parameters, resorting to linear-optical elements only. All these fourhyper-ECPs are feasible with current technology and they may be useful inlong-distance quantum communication based on hyperentanglement as they requireonly linear optical elements.

Hyperentanglement concentration for two-photon four-qubit systems with linear optics