Non-Markovianity and quantumness: Insights from dephasing channels

The description of how different quantum features, such as non-Markovianity and quantumness, interact in quantum channels is an important step in designing and managing quantum systems. Here, we look at three non-Markovian dephasing channels: pink, brown, and static noise. We investigate and evaluate various measures of non-Markovianity in these channels. Indeed, the proposed measurements include trace norm, entropy, and quantum capacity. We investigate the effect of non-Markovianity on the quantum nature of these channels. Our results show that increasing the degree of non-Markovianity in the suggested channels does not always improve the channel's quantumness. Furthermore, given the aforementioned quantum channels, the l2 norm of quantum coherence and mixedness satisfies the trade-off relation, which is critical for understanding how quantum resources and noise interact in open quantum systems.