Towards the standardization of quantum state verification using optimal strategies

Quantum devices for generating entangled states have been extensively studied and widely used. As so, it becomes necessary to verify that these devices truly work reliably and efficiently as they are specified. Here, we experimentally realize the recently proposed two-qubit entangled state verification strategies using both local measurements (nonadaptive) and active feed-forward operations (adaptive) with a photonic platform. About 3283/536 number of copies ($N$) are required to achieve a 99% confidence to verify the target quantum state for nonadaptive/adaptive strategies. These optimal strategies provide the Heisenberg scaling of the infidelity $\epsilon$ as a function of $N$ ($\epsilon$ $\sim$ $N^r$) with the parameter $r=-1$, exceeding the standard quantum limit with $r=-0.5$. We experimentally obtain the scaling parameter of $r=-0.88\pm$0.03 and $-0.78\pm$0.07 for nonadaptive and adaptive strategies, respectively. Our experimental work could serve as a standardized procedure for the verification of quantum states.