  High-dimensional entanglement is significant for the fundamental studies of
quantum physics and offers unique advantages in various quantum information
processing (QIP) tasks. Integrated quantum devices have recently emerged as a
promising platform for creating, processing, and detecting complex
high-dimensional entangled states. A crucial step towards practical quantum
technologies is to verify that these devices work reliably with an optimal
strategy. In this work, we experimentally implement an optimal quantum
verification strategy on a three-dimensional maximally entangled state using
local projective measurements on a silicon photonic chip. A 95% confidence is
achieved from 1190 copies to verify the target quantum state. The obtained
scaling of infidelity as a function of the number of copies is -0.5497+-0.0002,
exceeding the standard quantum limit of -0.5 with 248 standard deviations. Our
results indicate that quantum state verification could serve as an efficient
tool for complex quantum measurement tasks.
