The n-th decay rate of coherence for Bell-diagonal states under quantum channels
Huaijing Huang, Zhaoqi Wu, and Shao-Ming Fei
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Submission date: 12. Sep. 2020
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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 diﬀerent channels n times. We derive explicit formulas of the n-th decay rate based on l1 norm of coherence, relative entropy of coherence and skew information-based coherence. It is found that the larger the 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.