A dual formula for the noncommutative transport distance
Melchior Wirth
TL;DR
This paper establishes a duality formula for the noncommutative transport distance, extending the classical Wasserstein distance concepts into the quantum realm with entropic regularization.
Contribution
It introduces a duality formula for the noncommutative transport distance, akin to the dual Benamou-Brenier formulation in quantum settings.
Findings
Proves a duality formula for the noncommutative transport distance.
Connects the quantum transport distance to Hamilton-Jacobi-Bellmann equations.
Extends classical optimal transport concepts to noncommutative geometry.
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.
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