Abstract
We examine to what extent the l1 norm of coherence through an open quantum system is affected by noise. To discuss the effect of the noise, we give a definition of the decay rate of the l1 norm of coherence, i.e., the value of the coherence of initial states divided by the coherence of final states. Then we use the measure of the decay of coherence to discuss to what extent several noisy channels affects the coherence. We find that the decay rate is independent of the initial state parameters but only related to parameters of the phase flip channels, the depolarizing channels, and the amplitude channels. However, the decay rate is related to the initial state parameters and parameters of the bit flip channels. Contrary to the view at first glance, we find that the bit flip channels even have cohering power.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Horodecki, M., Oppenheim, J.: Description of quantum coherence in thermodynamic processes requires constraints beyond free energy. Nat. Commun. 4, 2059 (2013)
Lostaglio, M., Korzekwa, K., Jennings, D., Rudolph, T.: Quantum coherence, time-translation symmetry, and thermodynamics. Phys. Rev. X 5, 021001 (2015)
Rastegin, A.E.: Quantum-coherence quantifiers based on the Tsallis relative α entropies. Phys. Rev. A 93, 032136 (2016)
Åberg, J.: Quantifying superposition. arXiv:0612146
Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett. 113, 140401 (2014)
Winter, A., Yang, D.: Operational resource theory of coherence. Phys. Rev. Lett. 116, 120404 (2016)
Bromley, T.R., Cianciaruso, M., Adesso, G.: Frozen quantum coherence. Phys. Rev. Lett. 114, 210401 (2015)
Xi, Z.J.: Quantum coherence over the noisy quantum channels. Sci. China-Phys. Mech. Astron. 45, 030302 (2015). (in Chinese)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2010)
Acknowledgments
This work is supported by the Natural Science Foundation of China (Grant Nos. 61771294,61602232) and Shandong Provincial Natural Science Foundation, China (Grant No. ZR2015FQ006).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Gao, D., Xin, QL., Ye, ZL. et al. Decay Rate of the l1 Norm Coherence in Single-Qubit Systems. Int J Theor Phys 58, 1568–1575 (2019). https://doi.org/10.1007/s10773-019-04052-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-019-04052-4