On quantum versions of the classical Wasserstein distance

Abstract

We investigate a definition of quantum Wasserstein distance of two states based on their couplings on the product algebra as in the classical case. A detailed analysis of the two qubit model leads to a formal definition fulfilling some minimal requirements. It also shows that a clear-cut definition, by direct generalization of the classical one, is not achievable.

Julián Andrés Agredo Echeverry

Associate Professor