Improved precision-guaranteed quantum tomography

Quantum tomography is one of the standard tool in current quantum information experiments for verifying that a state/process/measurement prepared in the lab is close to an ideal target. Precision-guaranteed quantum tomography (Sugiyama, Turner, Murao, PRL 111, 160406 2013) gives rigorous error bars on a result estimated from arbitrary finite data sets from any given informationally complete tomography experiments. The rigorous error bars were derived with a real-valued concentration inequality called Hoeffding's inequality. In this talk, with a vector-valued concentration inequality, we provide an improved version of the error bars of precision-guaranteed quantum tomography. We examine the new error bars for specific cases of multi-qubit systems and numerically show that the degree of improvement becomes large as the dimension of the system increases.