Robustness of \(\varLambda \)-entanglement of multipartite states

  • Ying Yang
  • Huai-Xin CaoEmail author
  • Hui-Xian Meng


By introducing the relative robustness of \(\varLambda \)-entanglement of a multipartite state related to a \(\varLambda \)-separable state, the robustness of \(\varLambda \)-entanglement of a multipartite state is defined as the minimum of the relative robustness of \(\varLambda \)-entanglement of a state related to all \(\varLambda \)-separable states. It is proved that, as a function on the set of all quantum states of an n-partite system, robustness of \(\varLambda \)-entanglement is nonnegative, lower semi-continuous, and convex, and it is zero if and only if the state is \(\varLambda \)-separable. Thus, robustness of \(\varLambda \)-entanglement not only quantifies the endurance of \(\varLambda \)-entanglement of a state against linear noise, but also can be used to distinguish \(\varLambda \)-separable states from \(\varLambda \)-entangled states. Furthermore, influences of a quantum channel on robustness of \(\varLambda \)-entanglement are discussed.


\(\varLambda \)-separability \(\varLambda \)-entanglement Robustness Quantum channel 



This subject was supported by the National Natural Science Foundation of China (Nos. 11871318, 11771009, 11571213, 11601300) and the Fundamental Research Funds for the Central Universities (GK20181020, GK201801011), China Post-doctoral Science Foundation (No. 2018M631726), Shaanxi Province Innovation Ability Support Program (2018KJXX-054), and Subject Research Project of Yuncheng University (XK-2018032).


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Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceShaanxi Normal UniversityXi’anChina
  2. 2.School of Mathematics and Information TechnologyYuncheng UniversityYunchengChina

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