  Quantum state tomography via local measurements is an efficient tool for
characterizing quantum states. However it requires that the original global
state be uniquely determined (UD) by its local reduced density matrices (RDMs).
In this work we demonstrate for the first time a class of states that are UD by
their RDMs under the assumption that the global state is pure, but fail to be
UD in the absence of that assumption. This discovery allows us to classify
quantum states according to their UD properties, with the requirement that each
class be treated distinctly in the practice of simplifying quantum state
tomography. Additionally we experimentally test the feasibility and stability
of performing quantum state tomography via the measurement of local RDMs for
each class. These theoretical and experimental results advance the project of
performing efficient and accurate quantum state tomography in practice.

Quantum Physics