The swap transpose on couplings translates to Petz' recovery map on quantum channels
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arXiv
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| Format: | Preprint |
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2025
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| author | Bunth, Gergely Pitrik, József Titkos, Tamás Virosztek, Dániel |
| author_facet | Bunth, Gergely Pitrik, József Titkos, Tamás Virosztek, Dániel |
| contents | In [Ann. Henri Poincaré, {\bf 22} (2021), 3199-3234], De Palma and Trevisan described a one-to-one correspondence between quantum couplings and quantum channels realizing transport between states. The aim of this short note is to demonstrate that taking the Petz recovery map for a given channel and initial state is precisely the counterpart of the swap transpose operation on couplings. That is, the swap transpose of the coupling $Π_Φ$ corresponding to the channel $Φ$ and initial state $ρ$ is the coupling $Π_{rec}$ corresponding to the Petz recovery map $Φ_{rec}.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04919 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The swap transpose on couplings translates to Petz' recovery map on quantum channels Bunth, Gergely Pitrik, József Titkos, Tamás Virosztek, Dániel Mathematical Physics Operator Algebras Quantum Physics Primary: 49Q22, 81P16. Secondary: 81Q10 In [Ann. Henri Poincaré, {\bf 22} (2021), 3199-3234], De Palma and Trevisan described a one-to-one correspondence between quantum couplings and quantum channels realizing transport between states. The aim of this short note is to demonstrate that taking the Petz recovery map for a given channel and initial state is precisely the counterpart of the swap transpose operation on couplings. That is, the swap transpose of the coupling $Π_Φ$ corresponding to the channel $Φ$ and initial state $ρ$ is the coupling $Π_{rec}$ corresponding to the Petz recovery map $Φ_{rec}.$ |
| title | The swap transpose on couplings translates to Petz' recovery map on quantum channels |
| topic | Mathematical Physics Operator Algebras Quantum Physics Primary: 49Q22, 81P16. Secondary: 81Q10 |
| url | https://arxiv.org/abs/2512.04919 |