  Accurately estimating the overlap between quantum states is a fundamental
task in quantum information processing. While various strategies using distinct
quantum measurements have been proposed for overlap estimation, the lack of
experimental benchmarks on estimation precision limits strategy selection in
different situations. Here we compare the performance of four practical
strategies for overlap estimation, including tomography-tomography,
tomography-projection, Schur collective measurement and optical swap test. With
a photonic system, the overlap-dependent estimation precision for each strategy
is quantified in terms of the average estimation variance over uniformly
sampled states, which highlight the different performance of different
strategies. We further propose an adaptive strategy with optimized precision in
full-range overlap estimation. Our results shed new light on extracting the
parameter of interest from quantum systems, prompting the design of efficient
quantum protocols.
