Higher-order quantum information inequalities and error-correction of non-Markovian noise

arXiv:2611.05541v1 Announce Type: new Abstract: Defining entropy of a quantum channel has become a challenge with potential candidates recently reported in literature. In this Article, it is taken under consideration the entropy of a quantum channel defined as the quantum entropy of its associated Choi state. The consequences presented here of such approach is two-fold. First, the limitations on the information-processing of quantum channels are assessed, leading to the \emph{higher-order quantum information inequalities}. Those are then considered as useful witnesses of non-Markovian effects beyond a given number of quantum side-channels in a quantum process. Importantly, the presentation is given with the application of the methods for the study of examples.