  Optimizing the physical realization of quantum gates is important to build a
quantum computer. The controlled-SWAP gate, also named Fredkin gate, can be
widely applicable in various quantum information processing schemes. In the
present research, we propose and experimentally implement quantum Fredkin gate
in a single-photon hybrid-degrees-of-freedom system. Polarization is used as
the control qubit, and SWAP operation is achieved in a four-dimensional Hilbert
space spanned by photonic orbital angular momentum. The effective conversion
rate $\mathcal{P}$ of the quantum Fredkin gate in our experiment is $(95.4\pm
2.6)\%$. Besides, we find that a kind of Greenberger-Horne-Zeilinger-like
states can be prepared by using our quantum Fredkin gate, and these nonseparale
states can show its quantum contextual characteristic by the violation of
Mermin inequality. Our experimental design and coding method are useful for
quantum computing and quantum fundamental study in high-dimensional and hybrid
coding quantum systems.
