Improving application performance with biased distributions of quantum states

We consider the properties of a specific distribution mixed quantum states arbitrary dimension that can be biased towards mean purity. In particular, we analyze mixtures Haar-random pure with Dirichlet-distributed coefficients. analytically derive concentration parameters required to match purity Bures and Hilbert--Schmidt distributions in any dimension. Numerical simulations suggest this value recovers exactly, offering an alternative intuitive physical interpretation for ensembles Hilbert--Schmidt-distributed random states. then demonstrate how substituting these Dirichlet-weighted Haar place results measurable performance advantages machine-learning-based state tomography systems Bayesian reconstruction. Finally, experimentally characterize generated by both cloud-accessed IBM computer in-house source polarization-entangled photons. each case, our method more closely underlying than either or distributed various experimental conditions.