Summary form only given. The idea of quantum teleportation is to utilize the nonlocal correlations between an Einstein-Podolsky-Rosen pair of particles to prepare a quantum system in some state, which is the exact replica of an arbitrary unknown state of a distant individual system. Three experiments in this direction were published recently. In this paper, we experimentally demonstrate a quantum teleportation scheme which satisfies all four of the above conditions. The input state is an arbitrary polarization state and the BSM can distinguish all four orthogonal Bell states so that the state has a 100% certainty to be teleported in principle. This is because the BSM is based on nonlinear interactions which are necessary and non-trivial physical processes for correlating the input state and the entangled EPR pair.
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