Bures Projections: Closed-forms, Applications, and Manifestations

by Afham (Centre for Quantum Technologies, National University of Singapore)

Thursday Sep 11, 2025, 11:00 AM → 12:00 PM Europe/Paris

Salle de séminaire, bat. FERMI (LPT Toulouse)

We consider the projection, with respect to Bures distance, of PSD matrices onto various convex and compact sets, such as bipartite states with a given marginal and states with a given diagonal. We derive simple closed-form expressions for the projection, which is related to the saturation of the data processing inequality for fidelity. Applications include quantum process tomography and in constrained optimization problems involving PSD matrices and their ensembles, among others. 

Manifestations of the closed-form in existing literature include the generation of random channels and measurements, a 'normalization' to construct channels from CP maps, novel geometric and operational interpretations of PGM & Petz recovery map, and an information-geometric basis for the Leifer-Spekkens Bayesian quantum formalism, among others. 

We also expect relevance to classical ML due to the relation between Bures distance and the 2-Wasserstein distance.