Quantum Optimal Transport Barycenters: Existence, Duality, and Gaussian Rigidity
The research introduces a Quantum Optimal Transport (QOT) barycenter framework to generalize classical Wasserstein barycenters for quantum states and channels. It establishes existence and duality results, proving that under certain conditions, the resulting quantum state must be Gaussian. This framework links continuous-variable quantum systems to their classical limits via semiclassical convergence.