Strong Kantorovich duality for quantum optimal transport with generic cost and optimal couplings on quantum bits
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911628582191104 |
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| author | Bunth, Gergely Pitrik, József Titkos, Tamás Virosztek, Dániel |
| author_facet | Bunth, Gergely Pitrik, József Titkos, Tamás Virosztek, Dániel |
| contents | We prove Kantorovich duality for a linearized version of a recently proposed non-quadratic quantum optimal transport problem, where quantum channels realize the transport. As an application, we determine optimal solutions of both the primal and the dual problem using this duality in the case of quantum bits and distinguished cost operators, with certain restrictions on the states involved. Finally, keeping the same restrictions regarding the states involved, we use this information on optimal solutions to give an analytical proof of the triangle inequality even for the square of the induced quantum Wasserstein divergences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26326 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong Kantorovich duality for quantum optimal transport with generic cost and optimal couplings on quantum bits Bunth, Gergely Pitrik, József Titkos, Tamás Virosztek, Dániel Mathematical Physics Operator Algebras Quantum Physics Primary: 49Q22, 81P16. Secondary: 81Q10 We prove Kantorovich duality for a linearized version of a recently proposed non-quadratic quantum optimal transport problem, where quantum channels realize the transport. As an application, we determine optimal solutions of both the primal and the dual problem using this duality in the case of quantum bits and distinguished cost operators, with certain restrictions on the states involved. Finally, keeping the same restrictions regarding the states involved, we use this information on optimal solutions to give an analytical proof of the triangle inequality even for the square of the induced quantum Wasserstein divergences. |
| title | Strong Kantorovich duality for quantum optimal transport with generic cost and optimal couplings on quantum bits |
| topic | Mathematical Physics Operator Algebras Quantum Physics Primary: 49Q22, 81P16. Secondary: 81Q10 |
| url | https://arxiv.org/abs/2510.26326 |