Quantum memory precludes mixed-unitary dynamics
Abstract
Unital quantum channels, defined by their property of leaving the maximally mixed state invariant, form an important class of quantum operations. A distinguished subset of these channels can be represented as a probabilistic mixture of unitary evolutions. Characterizing channels that do not admit such a decomposition is in general a hard problem with significant implications for noise mitigation in quantum technologies and for fundamental problems in quantum information theory. Here we establish a link between mixed-unitarity of unital channels and the (quantum) nature of the memory effects in non-Markovian dynamics. Translating the problem into the language of process tensors, this connection yields a hierarchy of semidefinite programs that provides numerically efficient witnesses for non-mixed-unitary behavior, outperforming existing criteria. We demonstrate the power of this approach through illustrative examples of unital channels in dimensions three and four.
Cite
@article{arxiv.2603.17010,
title = {Quantum memory precludes mixed-unitary dynamics},
author = {Charlotte Bäcker and Konstantin Beyer and Walter T. Strunz},
journal= {arXiv preprint arXiv:2603.17010},
year = {2026}
}