A dual formula for the noncommutative transport distance

Understand

In this article we study the noncommutative transport distance introduced by Carlen and Maas and its entropic regularization defined by Becker and Li.

• We prove a duality formula that can be understood as a quantum version of the dual Benamou-Brenier formulation of the Wasserstein distance in terms of subsolutions of Hamilton-Jacobi-Bellmann equation.