Quantum Wasserstein isometries on the qubit state space
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914909996974080 |
|---|---|
| author | Gehér, György Pál Pitrik, József Titkos, Tamás Virosztek, Dániel |
| author_facet | Gehér, György Pál Pitrik, József Titkos, Tamás Virosztek, Dániel |
| contents | We describe Wasserstein isometries of the quantum bit state space with respect to distinguished cost operators. We derive a Wigner-type result for the cost operator involving all the Pauli matrices: in this case, the isometry group consists of unitary or anti-unitary conjugations. In the Bloch sphere model, this means that the isometry group coincides with the classical symmetry group $\mathbf{O}(3).$ On the other hand, for the cost generated by the qubit "clock" and "shift" operators, we discovered non-surjective and non-injective isometries as well, beyond the regular ones. This phenomenon mirrors certain surprising properties of the quantum Wasserstein distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_14134 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quantum Wasserstein isometries on the qubit state space Gehér, György Pál Pitrik, József Titkos, Tamás Virosztek, Dániel Mathematical Physics Functional Analysis Metric Geometry Quantum Physics Primary: 49Q22, 81Q99. Secondary: 54E40 We describe Wasserstein isometries of the quantum bit state space with respect to distinguished cost operators. We derive a Wigner-type result for the cost operator involving all the Pauli matrices: in this case, the isometry group consists of unitary or anti-unitary conjugations. In the Bloch sphere model, this means that the isometry group coincides with the classical symmetry group $\mathbf{O}(3).$ On the other hand, for the cost generated by the qubit "clock" and "shift" operators, we discovered non-surjective and non-injective isometries as well, beyond the regular ones. This phenomenon mirrors certain surprising properties of the quantum Wasserstein distance. |
| title | Quantum Wasserstein isometries on the qubit state space |
| topic | Mathematical Physics Functional Analysis Metric Geometry Quantum Physics Primary: 49Q22, 81Q99. Secondary: 54E40 |
| url | https://arxiv.org/abs/2204.14134 |