A Frame-Spread Lower Bound for Quantum Entropy Estimation under Fixed Rank-One Measurements
The study finds a lower bound for estimating quantum entropy using repeated, fixed rank-one measurements. It defines a metric called 'frame spread' ($\kappa_\nu$) to quantify measurement quality. The main result establishes that the minimum number of samples needed scales logarithmically with the dimension $d$, providing a crucial limit for quantum state estimation experiments.