Quantum Coherence in Non-Markovian Quantum Channels

Nana Zhang, Chao-Yi Wu, Xu Zhou +4 more

Chandan Datta, Sk Sazim, Arun Kumar Pati +1 more

He Zhi, Li Li, Chunmei Yao +1 more

We propose an approach to measuring non-Markovianity of an open two-level system from quantum coherence perspective including l1 norm of coherence and quantum relative entropy of coherence, and derive corresponding non-Markovian conditions. Further, as a particular application, non-Markovian conditions of an open two-level system undergoing phase damping channel, random unitary channel and amplitude damping channel, respectively are investigated. Specifically speaking, for the three channels we obtain non-Markovian conditions based on l1 norm of coherence at any initial state of system, and find that non-Markovian conditions are the same as the conditions of other measurements, i.e., information back-flow, divisibility and quantum mutual entropy for the phase damping channel and amplitude damping channel, but non-Markovian conditions new and different from the conditions of other measurements for random unitary channel. On the other hand, for phase damping channel we obtain non-Markovian conditions based on quantum relative entropy of coherence at any initial state of system, which are the same as the conditions of other measures, i.e., information back-flow, divisibility and quantum mutual entropy. However, for the random unitary channel and amplitude damping channel we obtain non-Markovian conditions at maximally coherent state of system.

Y. Aiache, C. Seida, K. El Anouz +1 more

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.

Javid Naikoo, Subhashish Banerjee

Yajing Fan, Lulu Li