Reduction of Measurement Complexity at Rank Reduction for Tomography of Polarization Qutrits in the Natural Basis

Tomography of polarization qutrits in a measurement scheme in a natural polarization basis with a minimum number of tunable elements has been investigated. The information completeness of protocols for states of various ranks has been analyzed theoretically using the analysis of the information matrix and compressive tomography methods was carried out; the results have been confirmed experimentally. The existence of a protocol with five dimensions that provides a complete reconstruction of arbitrary (including mixed) states has been shown, and it has been found that schemes with a smaller number of dimensions provide the complete reconstruction of pure states. The obtained protocols demonstrate high accuracy of reconstructing test states under the conditions of a limited set of rotations of the measuring basis.