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

• URL: http://arxiv.org/abs/2408.09879v1
• Date: Mon, 19 Aug 2024 10:41:32 GMT
• Title: Isometries of the qubit state space with respect to quantum Wasserstein distances
• Authors: Richárd Simon, Dániel Virosztek,
• Abstract summary: We study isometries of quantum Wasserstein distances and divergences on the quantum bit state space. We describe isometries with respect to the quantum symmetric Wasserstein divergence $d_sym$, the divergence induced by all of the Pauli matrices.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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