Interpolation of Density Matrices and Matrix-Valued Measures: The Unbalanced Case

2016/12/18 by Yongxin Chen, Tryphon T. Georgiou, Chen, Yongxin +3
Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.1612.05914

openalex publication_date 2016/12/18 · openalex created_date 2017/06/30 · openalex updated_date 2026/07/28

Abstract

In this note, we propose an unbalanced version of the quantum mechanical version of optimal mass transport that was based on the Lindblad equation. We formulate a natural interpolation framework between density matrices and matrix-valued measures via a quantum mechanical formulation of Fisher-Rao information and the matricial Wasserstein distance.

Citations

• An Interpolating Distance between Optimal Transport and Fisher-Rao
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Ricci curvature of Markov chains on metric spaces

Related

• Matrix Optimal Mass Transport: A Quantum Mechanical Approach
• Matricial Wasserstein-1 Distance
• Entropic and displacement interpolation: a computational approach using the Hilbert metric
• On the Role of Density Matrices in Bohmian Mechanics
• Unbalanced Optimal Transport: Dynamic and Kantorovich Formulation