Feasible noiseless linear amplification for single-photon qudit and two-photon hyperentanglement encoded in three degrees of freedom

Hyper-encoded photon qudits and hyperentanglement can effectively increase the channel capacity and have been widely used in quantum communication field. Photon transmission loss is one of the main obstacles of quantum communication, which can reduce the communication efficiency and even threaten the security. In the paper, we propose a feasible noiseless linear amplification (NLA) protocol for protecting the single-photon qudit and two-photon hyperentanglement encoded in polarization and double-longitudinal momentum degrees of freedom (DOFs). The NLA protocol is in linear optics, and especially, it adopts practical imperfect single photon sources to generate auxiliary photons. As a result, it can be realized under current experimental condition. By performing the NLA protocol, we can increase the fidelity of target qudit and hyperentanglement and preserve their encoding features in all DOFs. This NLA protocol has application potential in current and future high-capacity quantum communication field.