Triangle-like inequalities related to coherence and entanglement negativity

  • Zhi-Xiang JinEmail author
  • Xianqing Li-Jost
  • Shao-Ming Fei


Quantum coherence and entanglement are two key features in quantum mechanics and play important roles in quantum information processing and quantum computation. We provide a general triangle-like inequality satisfied by the \(l_1\)-norm measure of coherence for convex combination of arbitrary n pure states of a quantum state \(\rho \). Furthermore, we present triangle-like inequality for the convex-roof extended negativity for any states of rank 2, which gives a positive answer to a conjecture raised in Dai et al. (Phys. Rev. A 96:062308, 2017). Detailed examples are given to illustrate the relations characterized by the triangle-like inequalities.


Triangle-like inequality Quantum coherence Convex-roof extended negativity 



The authors would like to thank the anonymous referees for their valuable comments which helped to improve the results of the manuscript. This work is supported by the NSF of China under Grant No. 11675113 and NSF of Beijing under No. KZ201810028042.


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Authors and Affiliations

  1. 1.School of Mathematical SciencesCapital Normal UniversityBeijingChina
  2. 2.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany
  3. 3.School of Mathematics and StatisticsHainan Normal UniversityHaikouChina

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