Quantum state tomography is both a crucial component in the field of quantum information and computation and a formidable task that requires an incogitable 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. 

1. D. Ahn, Y. S. Teo, H. Jeong (서울대), F. Bouchard, F. Hufnagel, E. Karimi (University of Ottawa), D. Koutný, J. Řeháček, Z. Hradil (Palacký University), G. Leuchs, and L. L. Sánchez-Soto(Max-Planck-Institut für die Physik des Lichts)

Phys. Rev. Lett. 122, 100404 (2019)

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.100404