Efficient hyperentanglement purification for three-photon systems with the fidelity-robust quantum gates and hyperentanglement link.

We present an efficient and faithful hyperentanglement purification protocol (hyper-EPP) for three-photon system in mixed hyperentangled Greenberger-Horne-Zeilinger states with bit-flip errors in both spatial-mode and polarization degrees of freedom (DOFs), resorting to the fidelity-robust quantum gates and hyperentanglement link. Our high-efficiency hyper-EPP comes from two aspects. One is to pump the higher-fidelity hyperentanglement from different three-photon systems into the same three-photon system with fidelity-robust swap gates, the other is to reproduce some hyperentangled three-photon systems from hyperentangled two-photon subsystems based on hyperentanglement link. Moreover, as the infidelity originating from imperfect single-photon scattering can be heralded as a failure by triggering a detector, our hyper-EPP operates faithfully with the present quantum circuits. Furthermore, our hyper-EPP can be directly extended to purify multiple photon systems entangled in one DOF or hyperentangled in multiple DOFs.

Robust hybrid hyper-controlled-not gates assisted by an input-output process of low-Q cavities.

The two or more degrees of freedoms (DOFs) of photon systems are very useful in hyperparallel photonic quantum computing to accomplish more quantum logic gate operations with less resource, and depress photonic dissipation noise in quantum information processing. We present some flexible and adjustable schemes for hybrid hyper-controlled-not (hyper-CNOT) gates assisted by low-Q cavities, on the two-photon systems in both the spatial-mode and the polarization DOFs. These hybrid spatial-polarization hyper-CNOT gates consume less quantum resource and are more robust against photonic dissipation noise, compared with the integration of two cascaded CNOT gates in one DOF. Besides, simultaneous counter-propagation of two photons economize extremely the operation time in the whole process of our schemes. Moreover, these quantum logic gates are more feasible for fast quantum operations in the weak-coupling region of the low-Q cavities with current experimental technology, which are much different from strong-coupling cases of the high-Q ones.