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arXiv · 2408.09879

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

Richárd Simon·Dániel Virosztek
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Abstract

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 $d_{sym}$, the divergence induced by all of the Pauli matrices. We also give a complete characterization of isometries with respect to $D_z$, the quantum Wasserstein distance corresponding to the single Pauli matrix $\sigma_z$.

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Richárd Simon, Dániel Virosztek. 2024-08-19. Isometries of the qubit state space with respect to quantum Wasserstein distances. https://doi.org/10.1016/j.laa.2025.03.004

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