Remote state preparation of three-dimensional optical vortices.

We propose a feasible scheme to remotely prepare three-dimensional (3D) optical vortex lines. Our scheme relies on the complete description of high-dimensional orbital angular momentum (OAM) entanglement in terms of the Laguerre-Gaussian modes. It is theoretically demonstrated that by simply changing the pump beam waist, we can remotely prepare the target photons in the vortex states of 3D interesting morphology, appearing as twisted vortex strands, separated vortex loops, and vortex link or knot. Furthermore, we employ the biphoton Klyshko picture to illustrate the conservation law of the OAM index ℓ and the spreading effect of the radial mode index p, where the Schmidt numbers are calculated to show the high-dimensional capacity of the quantum channels involved in the present remote state preparation.

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