ИСТИНА

Spatial degrees of freedom of photons are an attractive option for encoding of quantum information. They offer a naturally high-dimensional Hilbert space allowing for implementation of various multidimensional protocols. In classical optical communication spatial mode division multiplexing is used to increase the bandwidth of communication channels. Most of experimental implementations are based on orbital angular momentum, however any set of orthogonal spatial mode functions may be utilized for encoding/multiplexing. Most of the currently used methods of manipulation and detection of spatially encoded information utilize spatial phase holograms. Designing an efficient holographic filter for higher order spatial modes turns out to be a challenging task, especially when modes with complicated radial field distributions are considered. However, experiments at the single photon level and applications in quantum communication require efficient spatial mode detectors with low crosstalk and losses. We will discuss an experimental approach to detector tomography of holographic mode detectors. We propose and implement experimentally a protocol for reconstruction of the POVM elements for spatial modes detectors inspired by quantum detector tomography for photon counters. Our protocol reconstructs the POVM elements of a spatial filter composed of a mode-transforming phase hologram and a single-mode fiber (with mode coupling optics) in a basis of Hermite-Gaussian modes. It is highly practical, since it does not require anything except the displaced Gaussian beams. Experimental results for various types of holograms are presented and quantitatively compared. The results of the reconstruction may be used as a feedback for adaptive scheme of designing a desired mode filter. We discuss the performance of such adaptive strategy and its application to design of an ideal Schmidt mode filter for the biphoton state.