Matrix Optimal Mass Transport: A Quantum Mechanical Approach

10 Oct 2016 Chen Yongxin Georgiou Tryphon T. Tannenbaum Allen

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... (read more)

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  • MATHEMATICAL PHYSICS
  • FUNCTIONAL ANALYSIS
  • MATHEMATICAL PHYSICS
  • OPTIMIZATION AND CONTROL