Matrix Optimal Mass Transport: A Quantum Mechanical Approach
Mathematical Physics
2016-10-11 v1 Functional Analysis
math.MP
Optimization and Control
Abstract
In this paper, we describe a possible generalization of the Wasserstein 2-metric, originally defined on the space of scalar probability densities, to the space of Hermitian matrices with trace one, and to the space of matrix-valued probability densities. Our approach follows a computational fluid dynamical formulation of the Wasserstein-2 metric and utilizes certain results from the quantum mechanics of open systems, in particular the Lindblad equation. It allows determining the gradient flow for the quantum entropy relative to this matricial Wasserstein metric. This may have implications to some key issues in quantum information theory.
Cite
@article{arxiv.1610.03041,
title = {Matrix Optimal Mass Transport: A Quantum Mechanical Approach},
author = {Yongxin Chen and Tryphon T. Georgiou and Allen Tannenbaum},
journal= {arXiv preprint arXiv:1610.03041},
year = {2016}
}
Comments
19 pages