Characterizing quantum states is a central, yet involved, task in quantum information processing. In experiments, the unknown quantum state of interest must be prepared and measured multiple times...Show moreCharacterizing quantum states is a central, yet involved, task in quantum information processing. In experiments, the unknown quantum state of interest must be prepared and measured multiple times to learn its properties. Unfortunately, a full tomographic description is prohibitive by the exponential scaling of the quantum state description with the system size. In practice, only a few quantities are of interest for which protocols involving informationally incomplete measurements are preferable. After studying existing data acquisition protocols, we discuss classical shadow estimation, a particular experimentally feasible method for estimating many system properties. We extend the applicability to quantum many-body systems with higher dimensional subspaces and derive similar performance guarantees to the qubit case. Ultimately we implement the generalized protocol in a modular and economic numerical framework and demonstrate the accuracy along with the favourable scaling of classical shadow estimation in unbiased numerical experiments. In particular, we suggest and discuss the near-term application to 4-photon OAM entangled systems.Show less
