Quantum Wasserstein-1 Distance

Yongxin Chen, Tryphon T. Georgiou, Lipeng Ning, Allen Tannenbaum

Published 2017-02-25Version 1

In this note, we propose an extension of the Wasserstein 1-metric ($W_1$) for matrix probability densities, matrix-valued density measures, and an unbalanced interpretation of mass transport. The key is using duality theory, in particular, a "dual of the dual" formulation of $W_1$. This matrix analogue of the Earth Mover's Distance has several attractive features including ease of computation.