  Quantum teleportation provides a "disembodied" way to transfer quantum states
from one object to another at a distant location, assisted by priorly shared
entangled states and a classical communication channel. In addition to its
fundamental interest, teleportation has been recognized as an important element
in long-distance quantum communication, distributed quantum networks and
measurement-based quantum computation. There have been numerous demonstrations
of teleportation in different physical systems such as photons, atoms, ions,
electrons, and superconducting circuits. Yet, all the previous experiments were
limited to teleportation of one degree of freedom (DoF) only. However, a single
quantum particle can naturally possess various DoFs -- internal and external --
and with coherent coupling among them. A fundamental open challenge is to
simultaneously teleport multiple DoFs, which is necessary to fully describe a
quantum particle, thereby truly teleporting it intactly. Here, we demonstrate
the first teleportation of the composite quantum states of a single photon
encoded in both the spin and orbital angular momentum. We develop a method to
project and discriminate hyper-entangled Bell states exploiting probabilistic
quantum non-demolition measurement, which can be extended to more DoFs. We
verify the teleportation for both spin-orbit product states and hybrid
entangled state, and achieve a teleportation fidelity ranging from 0.57 to
0.68, above the classical limit. Our work moves a step toward teleportation of
more complex quantum systems, and demonstrates an enhanced capability for
scalable quantum technologies.
