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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2408.09879 |
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| _version_ | 1866908288550961152 |
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| author | Simon, Richárd Virosztek, Dániel |
| author_facet | Simon, Richárd Virosztek, Dániel |
| contents | 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 $σ_z$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09879 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Isometries of the qubit state space with respect to quantum Wasserstein distances Simon, Richárd Virosztek, Dániel Mathematical Physics Functional Analysis Metric Geometry Quantum Physics Primary: 49Q22, 81Q99. Secondary: 54E40 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 $σ_z$. |
| title | Isometries of the qubit state space with respect to quantum Wasserstein distances |
| topic | Mathematical Physics Functional Analysis Metric Geometry Quantum Physics Primary: 49Q22, 81Q99. Secondary: 54E40 |
| url | https://arxiv.org/abs/2408.09879 |