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Structure photons invoke interesting fundamental properties and enable novel applications, e.g. their use as high-dimensional quantum states, which are known to be beneficial in various quantum information tasks. However, to use their full potential the ability to perform any unitary operations is indispensable.
Here, we present a scheme to perform arbitrary unitary operation for all transverse spatial modes, i.e. a so-called multiport for high-dimensional quantum states. We realize it by using multiple consecutive phase modulations, which are designed by wave front matching techniques.
At first, we perform near-perfect measurements of full-field modes, i.e. modes with an azimuthal and radial structure [1]. Our method only requires three consecutive phase modulations followed by a single mode fiber and is, in principle, error-free and lossless. We achieve an average error of 4.2% for a set of 9 different full-field Laguerre-Gauss and Hermite-Gauss modes with an efficiency of up to 70%. We further demon-strate its potential in a quantum cryptography protocol and in high-dimensional quantum state tomography.
We then use the multiport to implement high-dimensional quantum gates [2], such as cyclic and quantum Fourier transformations, known as Pauli X-gates and Hadamard H-gates, respectively. We achieve an aver-age visibility of more than 90% for dimensions up to 5 and obtain a process purity of 99% by means of a full quantum process tomography. We also demonstrate the benefit of the two independent spatial degrees of freedom, i.e. azimuthal and radial, and implement a two-qubit controlled-NOT quantum operation on a single photon.
Using more efficient phase modulations will pave the way to novel multi-particle high-dimensional quantum information experiments.
[1] M. Hiekkamäki, S. Prabhakar, R. Fickler, Near-perfect measuring of full-field transverse-spatial modes of light, arXiv:1909.01685
[2] F. Brandt, M. Hiekkamäki, F. Bouchard, M. Huber, R. Fickler, High-dimensional quantum gates using full-field spatial modes of photons, arXiv:1907.13002
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