Exact Posterior Prediction from Product Haar Measurements and a Randomized-Mesh Maximum-Likelihood Bridge
The study predicts an unknown quantum state by measuring its copies using a fixed product Haar measurement. The exact prediction is a full-rank state derived from Gram-matrix combinatorics, proving its positivity and normalization. Performance guarantees show that the risk scales as O((d^2/epsilon) log(d/epsilon)), connecting fine product data to sharp asymptotic bounds via randomized meshes.