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

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. Second, such approach provides a characterization on the condition for the recovery of quantum channel preparations under non-Markovian noise. Such result is a straightforward extension of standard error-correction conditions which gives further meaning to the higher-order information measures defined here.