We consider six-photon entangled state emitted from a single third-order parametric down-conversion process. In the regime of weak nonlinearities, we present a symmetry detector which is capable of analyzing the twin-beam six-photon symmetric states. By cascading the symmetry detectors, as an application, it is shown that one can purify the desired six-photon entangled state from an arbitrary twin-beam six-photon symmetric state. With linear optics we propose a fruitful scheme for exploring a class of multimode-photon entangled states from third-order parametric down-conversion process. Furthermore, we provide a method to generate the six-photon polarization entangled Greenberger-Horne-Zeilinger state based on linear optics and weak nonlinearities.
@article{arxiv.2003.00797,
title = {On six-photon entangled state emitted from a single third-order parametric down-conversion process},
author = {Ying-Qiu He and Dong Ding and Ting Gao and Fengli Yan},
journal= {arXiv preprint arXiv:2003.00797},
year = {2021}
}