The swap transpose on couplings translates to Petz' recovery map on quantum channels
Mathematical Physics
2025-12-12 v2 math.MP
Operator Algebras
Quantum Physics
Abstract
In [Ann. Henri Poincar\'e, {\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 corresponding to the channel and initial state is the coupling corresponding to the Petz recovery map
Keywords
Cite
@article{arxiv.2512.04919,
title = {The swap transpose on couplings translates to Petz' recovery map on quantum channels},
author = {Gergely Bunth and József Pitrik and Tamás Titkos and Dániel Virosztek},
journal= {arXiv preprint arXiv:2512.04919},
year = {2025}
}
Comments
11 pages. v2: References to the closely related works [Duvenhage et al., Quantum 9, 1743 (2025)] and [Parzygnat et al., PRX Quantum 4, 020334 (2023)] have been included