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Superadditivity relations of the \(l_1\) norm of coherence

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Abstract

Quantum coherence is an important physical resource in quantum computation and quantum information processing. Among the appropriate measures of quantum coherence, the \(l_1\) norm of coherence is a widely known coherence measure and easy to use quantifiers. In this paper, we discuss the superadditivity inequalities and strong subadditivity of the \(l_1\) norm of coherence. We show that the \(l_1\) norm of coherence is superadditive for all states, which gives a positive answer to a conjecture in Liu and Li (Int J Theor Phys 56:494, 2017).

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Acknowledgements

This work is supported by NSFC (Grant Nos. 61771294, 61202475, 11501404) and Shandong Provincial Natural Science Foundation, China (Grant No. ZR2015FQ006) and Higher Educational Science and Technology Program of Hebei Province (Grant No. QN2015303).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao, 066004, China

    Pi-Yu Li & Yan-Qin Xu

  2. College of Mathematic and Information Science, Shandong Technology and Business University, Yantai, 264005, China

    Feng Liu

Authors
  1. Pi-Yu Li
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  2. Feng Liu
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  3. Yan-Qin Xu
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Correspondence to Feng Liu.

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Li, PY., Liu, F. & Xu, YQ. Superadditivity relations of the \(l_1\) norm of coherence. Quantum Inf Process 17, 18 (2018). https://doi.org/10.1007/s11128-017-1790-9

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  • DOI: https://doi.org/10.1007/s11128-017-1790-9

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