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Hyperentanglement, defined as the simultaneous entanglement in severalindependent degrees of freedom (DOFs) of a quantum system, is a fascinatingresource in quantum information processing with its outstanding merits. Here wepropose heralded hyperentanglement concentration protocols (hyper-ECPs) toconcentrate an unknown partially less polarization-spatial hyperentangled Bellstate with available linear optics and common single-photon detectors. Byintroducing time-delay DOFs, the schemes are highly efficient in that thesuccess of the scheme can be accurately heralded by the detection signatures,and postselection techniques or photon-number-resolving detectors, necessaryfor previous experiments, are not required. Additionally, our linear opticalarchitectures allow certain states, where concentration fails, to berecyclable, and a trick makes the success probabilities of our schemes higherthan those of previous linear optical hyper-ECPs.

Practically Enhanced Hyperentanglement Concentration for  Polarization-spatial Hyperentangled Bell States with Linear Optics and Common  Single-photon Detectors