International Journal of Theoretical Physics

, Volume 58, Issue 12, pp 3998–4007 | Cite as

A Note on the Relationship Between Genuinely Coherence and Generalized Entanglement Monotones

  • Jiahuan Qiao
  • Zong Wang
  • Jing WangEmail author
  • Ming Li
  • Shuqian Shen
  • Zhihao Ma


We find a one to one mapping between genuinely incoherent operations and special one-way local operations and classical communication(LOCC) for density matrices with full rank. We also define “generalized entanglement monotones” and “genuinely coherence monotones” under special one-way LOCC and genuinely incoherent operations respectively. Any entanglement monotone proposed by Vidal et al. is a generalized entanglement monotone. Any coherence monotone under incoherent operations is a genuinely coherence monotone. Furthermore, we clarify the relationship between generalized entanglement monotones and genuinely coherence monotones. We demonstrate that any generalized entanglement monotone of bipartite pure state is the lower bound of a suitable genuinely coherence monotone; any genuinely coherence monotone of a quantum state is the generalized entanglement monotone of the corresponding maximally correlated state.


Quantum coherence Quantum entanglement LOCC 



This work is supported by the NSFC No.11775306, and 11701568; the Fundamental Research Funds for the Central Universities Grants No. 17CX02033A and 19CX02050A; the Shandong Provincial Natural Science Foundation No.ZR2016AQ06, and ZR2017BA019.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Jiahuan Qiao
    • 1
  • Zong Wang
    • 1
  • Jing Wang
    • 1
    Email author
  • Ming Li
    • 1
    • 2
  • Shuqian Shen
    • 1
  • Zhihao Ma
    • 3
  1. 1.College of the ScienceChina University of PetroleumQingdaoChina
  2. 2.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany
  3. 3.Math DepartmentShanghai Jiaotong UniversityShanghaiChina

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