Paper
The swap transpose on couplings translates to Petz' recovery map on quantum channels
Authors
Gergely Bunth, József Pitrik, Tamás Titkos, Dániel Virosztek
Abstract
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 corresponding to the channel and initial state is the coupling corresponding to the Petz recovery map