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Super-Additivity Relations and Decay of the l 1 Norm of Coherence

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Abstract

The l 1 norm of coherence and the relative entropy of coherence are the most general and easy to use quantifiers. Based on the l 1 norm of coherence, we discuss the super-additivity inequalities and then give the explicit characterization of three-qubit pure states saturating these relations. We also prove that the l 1 norm of coherence is super-additive for all pure states and qubit states. Further, we use the measure of the decay of quantum coherence to discuss how well ideal models of noise preserve the relative entropy of coherence on pure single-qubit sysrems.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 60973135 and 61602232) and Shandong Provincial Natural Science Foundation, China (Grant No. ZR2015FQ006).

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Authors and Affiliations

  1. College of Mathematic and Information Science, Shandong Institute of Business and Technology, Yantai, 264005, China

    Feng Liu

  2. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510000, China

    Fei Li

  3. School of Mathematics and Statistics Science, Ludong University, Yantai, 264025, China

    Fei Li

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  1. Feng Liu
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  2. Fei Li
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Correspondence to Feng Liu.

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Liu, F., Li, F. Super-Additivity Relations and Decay of the l 1 Norm of Coherence. Int J Theor Phys 56, 494–502 (2017). https://doi.org/10.1007/s10773-016-3190-9

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  • DOI: https://doi.org/10.1007/s10773-016-3190-9

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