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arXiv · 2512.04919

The swap transpose on couplings translates to Petz' recovery map on quantum channels

Gergely Bunth·József Pitrik·Tamás Titkos·Dániel Virosztek
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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 $\Pi_{\Phi}$ corresponding to the channel $\Phi$ and initial state $\rho$ is the coupling $\Pi_{rec}$ corresponding to the Petz recovery map $\Phi_{rec}.$

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Gergely Bunth, József Pitrik, Tamás Titkos, Dániel Virosztek. 2025-12-04. The swap transpose on couplings translates to Petz' recovery map on quantum channels. https://arxiv.org/abs/2512.04919

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