The nth Decay Rate of Coherence for Belldiagonal States Under Quantum Channels
Abstract
We study the degree to which the coherence of quantum states is affected by noise. We give the definition of the nth decay rate and investigate the coherence of Belldiagonal states under n iterations of channels. We derive explicit formulas of the nth decay rates based on l_{1} norm of coherence, relative entropy of coherence and skew informationbased coherence. It is found that the larger n is, the faster the nth decay rate decreases as the parameter p of Belldiagonal states increases. Moreover, for any fixed n, with the increase of p, Belldiagonal 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 bitphase flip (BPF) channels. We also investigate the geometry of the relative entropy of coherence and skew informationbased coherence of Belldiagonal states under different channels when the nth 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 Belldiagonal states will not be frozen under GAD, DEP and PF channels. For skew informationbased coherence, similar properties of coherence freezing are found.
 Publication:

International Journal of Theoretical Physics
 Pub Date:
 July 2020
 DOI:
 10.1007/s10773020045519
 arXiv:
 arXiv:2009.01503
 Bibcode:
 2020IJTP...59.2912H
 Keywords:

 Decay rate;
 Quantum coherence;
 Belldiagonal state;
 Quantum channel;
 Frozen coherence;
 Quantum Physics
 EPrint:
 International Journal of Theoretical Physics (2020) 59:29122923