Quantum state tomography is both a crucial component in the field of quantum information and computation, and a formidable task that requires an incogitably large number of measurement configurations as the system dimension grows. We propose and experimentally carry out an intuitive adaptive compressive tomography scheme, inspired by the traditional compressed-sensing protocol in signal recovery, that tremendously reduces the number of configurations needed to uniquely reconstruct any given quantum state without any additional a priori assumption whatsoever (such as rank information, purity, etc) about the state, apart from its dimension.
@article{arxiv.1812.05289,
title = {Adaptive compressive tomography with no a priori information},
author = {D. Ahn and Y. S. Teo and H. Jeong and F. Bouchard and F. Hufnagel and E. Karimi and D. Koutny and J. Rehacek and Z. Hradil and G. Leuchs and L. L. Sanchez-Soto},
journal= {arXiv preprint arXiv:1812.05289},
year = {2019}
}