• DOI:10.1007/s10773-020-04551-9
• Corpus ID: 225370038

The n-th Decay Rate of Coherence for Bell-diagonal States Under Quantum Channels

@article{Huang2020TheND,
  title={The n-th Decay Rate of Coherence for Bell-diagonal States Under Quantum Channels},
  author={Huaijing Huang and Zhaoqi Wu and Shao-Ming Fei},
  journal={International Journal of Theoretical Physics},
  year={2020},
  volume={59},
  pages={2912 - 2923}
}

• Huaijing Huang, Zhaoqi Wu, S. Fei
• Published 29 July 2020
• Physics
• International Journal of Theoretical Physics

We study the degree to which the coherence of quantum states is affected by noise. We give the definition of the n-th decay rate and investigate the coherence of Bell-diagonal states under n iterations of channels. We derive explicit formulas of the n-th decay rates based on l1 norm of coherence, relative entropy of coherence and skew information-based coherence. It is found that the larger n is, the faster the n-th decay rate decreases as the parameter p of Bell-diagonal states increases. Moreover, for any fixed n, with the increase of p, Bell-diagonal states can be completely incoherent under generalized amplitude damping (GAD) channels, depolarization (DEP) channels and phase flip (PF) channels, while this is not the case for bit flip (BF) channels and bit-phase flip (BPF) channels. We also investigate the geometry of the relative entropy of coherence and skew information-based coherence of Bell-diagonal states under different channels when the n-th decay rate is one, i.e., the coherence is frozen. It is shown that compared with BF and BPF channels, when n is large enough, the coherence of Bell-diagonal states will not be frozen under GAD, DEP and PF channels. For skew information-based coherence, similar properties of coherence freezing are found.