Joint BCAM-UPV/EHU Analysis and PDE seminar: On quantum Wasserstein distance

A classical Wasserstein distance is a metric between two probability distributions, induced by the problem of optimal mass transportation. It reflects the minimal effort that is required in order to morph the mass of the first probability distribution into the mass of the other one. 

Optimal transport is a central problem in mathematics and engineering, which has been generalized to the quantum setting. The quantum

Wasserstein distance has recently been defined based on a minimization of a cost operator over bipartite states with given marginals, such that it is also related to quantum channel formalism. It has been found that in this case the self-distance of the state is nonzero and equals

the Wigner-Yanase skew information. If we restrict the optimization to separable states then, surprisingly, the self-distance is related to the quantum Fisher information, a quantity central to quantum metrology. 

The talk is based on the common work with Géza Tóth, Dániel Virosztek and Tamás Titkos.