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.
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BibTeX
@misc{capela2026higherorder,
title = {{Higher-order quantum information inequalities and error-correction of non-Markovian noise}},
author = {Matheus Capela},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05541},
eprint = {2611.05541},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05541},
}
RIS
TY - UNPB
TI - Higher-order quantum information inequalities and error-correction of non-Markovian noise
AU - Matheus Capela
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05541
UR - https://arxiv.org/abs/2611.05541
AB - 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.
ER -