Realization of quantum permutation algorithm in high dimensional Hilbert space

Quantum algorithms provide a more efficient way to solve computational tasks than classical algorithms. We experimentally realize quantum permutation algorithm using light's orbital angular momentum degree of freedom. By exploiting the spatial mode of photons, our scheme provides a more elegant way to understand the principle of quantum permutation algorithm and shows that the high dimension characteristic of light's orbital angular momentum may be useful in quantum algorithms. Our scheme can be extended to higher dimension by introducing more spatial modes and it paves the way to trace the source of quantum speedup.     

Subwavelength Fourier-transform imaging without a lens or a beamsplitter

The fourier-transform patterns of an object are usually observed in the far-field region or obtained in the near-field region with the help of lenses. Here we propose and experimentally demonstrate a scheme of Fourier-transform patterns in the Fresnel diffraction region with thermal light. In this scheme, neither a lens nor a beamsplitter is used, and only one single charge coupled device(CCD) is employed. It means that dividing one beam out of a light source into signal and reference beams is not as necessary as the one done by the use of a beamsplitter in usual ghost interference experiments.Moreover, the coincidence measurement of two point detectors is not necessary and data recorded on a single CCD are sufficient for reconstructing the ghost diffraction patterns. The feature of the scheme promises a great potential application in the fields of X-ray and neutron diffraction imaging processes.