The verification of a requirement of entanglement measures

@article{Qi2021TheVO,
  title={The verification of a requirement of entanglement measures},
  author={Xianfei Qi and Ting Gao and Fengli Yan},
  journal={Quantum Inf. Process.},
  year={2021},
  volume={20},
  pages={133}
}
The quantification of quantum entanglement is a central issue in quantum information theory. Recently, Gao \emph{et al}. ( \href{this http URL}{Phys. Rev. Lett. \textbf{112}, 180501 (2014)}) pointed out that the maximum of entanglement measure of the permutational invariant part of $\rho$ ought to be a lower bound on entanglement measure of the original state $\rho$, and proposed that this argument can be used as an additional requirement for (multipartite) entanglement measures. Whether any… 
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