Isometries of the qubit state space with respect to quantum Wasserstein distances

In this paper we study isometries of quantum Wasserstein distances and divergences on the quantum bit state space. We describe isometries with respect to the symmetric quantum Wasserstein divergence dsym, the divergence induced by all of the Pauli matrices. We also give a complete characterization of isometries with respect to Dz, the quantum Wasserstein distance corresponding to the single Pauli matrix σz.