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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
92/2020

The $n$-th decay rate of coherence for Bell-diagonal states under quantum channels

Huaijing Huang, Zhaoqi Wu and Shao-Ming Fei

Abstract

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 $l_1$ 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.

Received:
Sep 12, 2020
Published:
Sep 27, 2020

Related publications

inJournal
2020 Repository Open Access
Huai-Jing Huang, Zhaoqi Wu and Shao-Ming Fei

The n-th decay rate of coherence for Bell-diagonal states under quantum channels

In: International journal of theoretical physics, 59 (2020) 9, pp. 2912-2923