Statistical inference for Bures–Wasserstein barycenters

In this work we introduce the concept of Bures–Wasserstein barycenter Q∗, that is essentially a Fréchet mean some distribution P supported on subspace positive semi-definite d-dimensional Hermitian operators H+(d). We allow to be constrained affine H+(d), and provide conditions ensuring its existence uniqueness. also investigate convergence concentration properties an empirical counterpart Q∗ in both Frobenius norm distance, explain, how obtained results are connected optimal transportation theory can applied statistical inference quantum mechanics.