Tighter generalized monogamy and polygamy relations for multiqubit systems

  • Zhi-Xiang JinEmail author
  • Shao-Ming FeiEmail author


We present a different kind of monogamy and polygamy relations based on concurrence and concurrence of assistance for multiqubit systems. By relabeling the subsystems associated with different weights, a smaller upper bound of the \(\alpha \)th (\(0\le \alpha \le 2\)) power of concurrence for multiqubit states is obtained. We also present tighter monogamy relations satisfied by the \(\alpha \)th (\(0\le \alpha \le 2\)) power of concurrence for N-qubit pure states under the partition AB and \(C_1 \cdots C_{N-2}\), as well as under the partition \(ABC_1\) and \(C_2\cdots C_{N-2}\). These inequalities give rise to the restrictions on entanglement distribution and the trade-off of entanglement among the subsystems. Similar results are also derived for negativity.


Entanglement monogamy Entanglement polygamy Concurrence Convex-roof extended negativity 



This work is supported by the NSF of China under Grant Nos. 11847209; 11675113; Beijing Municipal Commission of Education (KM201810011009); Beijing Natural Science Foundation (Z190005) and the China Postdoctoral Science Foundation funded project.


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Authors and Affiliations

  1. 1.School of Mathematical SciencesCapital Normal UniversityBeijingChina
  2. 2.School of PhysicsUniversity of Chinese Academy of SciencesBeijingChina
  3. 3.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany

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