Quantum optimal transport (QOT) extends classical transport theory to the non-commutative setting, introducing new challenges in optimization and analysis. In this talk, I will focus on our duality results for QOT with general convex regularization. We establish the existence and characterization of solutions for both the primal and dual problems.
To illustrate the key ideas, I will first present the proof strategy for the strictly convex and differentiable case, highlighting the main techniques involved. We will then briefly discuss how these results extend to general convex regularization.
Additionally, I will mention our results on unbalanced QOT, including the convergence of solutions as the marginal penalization parameter $\tau$ tends to infinity.
This talk is based on a joint publication with E. Caputo, A. Gerolin, and L. Portinale.
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