  Quantum state verification provides an efficient approach to characterize the
reliability of quantum devices for generating certain target states. The figure
of merit of a specific strategy is the estimated infidelity $\epsilon$ of the
tested state to the target state, given a certain number of performed
measurements n. Entangled measurements constitute the globally optimal strategy
and achieve the scaling that \epsilon is inversely proportional to n. Recent
advances show that it is possible to achieve the same scaling simply with
non-adaptive local measurements, however, the performance is still worse than
the globally optimal bound up to a constant factor. In this work, by
introducing classical communication, we experimentally implement an adaptive
quantum state verification. The constant-factor is minimized from ~2.5 to 1.5
in this experiment, which means that only 60% measurements are required to
achieve a certain value of \epsilon compared to optimal non-adaptive local
strategy. Our results indicate that classical communication significantly
enhances the performance of quantum state verification, and leads to an
efficiency that further approaches the globally optimal bound.
