  The initialization of a quantum system into a certain state is a crucial
aspect of quantum information science. While a variety of measurement
strategies have been developed to characterize how well the system is
initialized, for a given one, there is in general a trade-off between its
efficiency and the accessible information of the quantum state. Conventional
quantum state tomography can characterize unknown states by reconstructing the
density matrix; however, its exponentially expensive postprocessing is likely
to produce a deviate result. Alternatively, quantum state verification provides
a technique to quantify the prepared state with significantly fewer
measurements, especially for quantum entangled states. Here, we experimentally
implement an optimal verification of entangled states with local measurements,
where the estimated infidelity is inversely proportional to the number of
measurements. The utilized strategy is tolerant of the impurity of realistic
states, hence being highly robust in a practical sense. Even more valuable, our
method only requires local measurements, which incurs only a small
constant-factor (<2.5) penalty compared to the globally optimal strategy
requiring nonlocal measurements.
