A dual formula for the noncommutative transport distance

Abstract

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.

References in corpus (2)

• Quadratic Wasserstein metrics for von Neumann algebras via transport plans
• Quantum statistical learning via Quantum Wasserstein natural gradient

Cited by in corpus (4)

• Improving the speed of variational quantum algorithms for quantum error correction
• The Wasserstein distance of order 1 for quantum spin systems on infinite lattices
• Ricci curvature of quantum channels on non-commutative transportation metric spaces
• Classical shadows meet quantum optimal mass transport