Adaptive quantum tomography of high-dimensional bipartite systems

Adaptive measurements have recently been shown to significantly improve the performance of quantum state and process tomography. Adaptive tomography is especially useful in complicated experiments with low outcome generation rate, since it allows one to extract maximal information from a limited amount of data. However, the existing methods either cannot be simply applied to high-dimensional systems or are prohibitively computationally expensive. Here we propose and experimentally implement a tomographic protocol specially designed for the reconstruction of high-dimensional quantum states. The protocol shows qualitative improvement in infidelity scaling with the number of measurements and is fast enough to allow for complete state tomography of states with dimensionality up to 36.