General hyperconcentration of photonic polarization-time-bin hyperentanglement assisted by nitrogen-vacancy centers coupled to resonators

Entanglement concentration protocol (ECP) is used to extract the maximally entangled states from less entangled pure states. Here we present a general hyperconcentration protocol for two-photon systems in partially hyperentangled Bell states that decay with the interrelation between the time-bin and the polarization degrees of freedom (DOFs), resorting to an input-output process with respect to diamond nitrogen-vacancy centers coupled to resonators. We show that the resource can be utilized sufficiently and the success probability is largely improved by iteration of the hyper-ECP process. Besides, our hyper-ECP can be directly extended to concentrate nonlocal partially hyperentangled N-photon Greenberger-Horne-Zeilinger states, and the success probability remains unchanged with the growth of the number of photons. Moreover, the time-bin entanglement is a useful DOF and it only requires one path for transmission, which means it not only economizes on a large amount of quantum resources but also relaxes from the path-length dispersion in long-distance quantum communication.