Author(s): Giorgio Stucchi, J. Ignacio Cirac, Rahul Trivedi, and Georgios Styliaris We develop a framework for matrix product quantum channels, a one-dimensional tensor-network description of completely positive, trace-preserving maps. We focus on translation-invariant channels, generated by a single repeated tensor, that admit a local purification. We show that their purifying iso… [Phys. Rev. Lett. 137, 120401] Published Wed Sep 16, 2026