A simple and flexible scheme for high-dimensional linear quantum operations on optical transverse spatial modes is demonstrated. The quantum Fourier transformation (QFT) and quantum state tomography (QST) via symmetric informationally complete positive operator-valued measures (SIC POVMs) are implemented with dimensionality of 15. The matrix fidelity of QFT is 0.85, while the statistical fidelity of SIC POVMs and fidelity of QST are ~0.97 and up to 0.853, respectively. We believe that our device has the potential for further exploration of high-dimensional spatial entanglement provided by spontaneous parametric down conversion in nonlinear crystals.
@article{arxiv.2005.06783,
title = {Programmable coherent linear quantum operations with high-dimensional optical spatial modes},
author = {Shikang Li and Shan Zhang Xue Feng and Stephen M. Barnett and Wei Zhang and Kaiyu Cui and Fang Liu and Yidong Huang},
journal= {arXiv preprint arXiv:2005.06783},
year = {2020}
}