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<p>We study the robustness of genuine multipartite entanglement and inseparability of multipartite pure states under superposition with product pure states. We introduce the concept of the maximal and the minimal Schmidt ranks for multipartite states. From the minimal Schmidt rank of the first order we present criterion of verifying unconditional robustness of genuine multipartite entanglement of multipartite pure states under superposition with product pure states. By the maximal Schmidt rank of the first order we verify the unconditional robustness of multipartite inseparability under superposition with product pure states. The number of product states superposed to a given entangled state which result in a separable state is investigated in detail. Furthermore the minimal Schmidt ranks of the second order are also introduced to identify the unconditional robustness of an entangled state for tripartite inseparability.</p>

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Unconditional robustness of multipartite entanglement of superposition

  • 期刊论文

  • 发表日期：

    2025年4月3日

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  • Hui-Hui Qin,
  • Shao-Shuai Zhao,
  • Shao-Ming Fei

摘要

We study the robustness of genuine multipartite entanglement and inseparability of multipartite pure states under superposition with product pure states. We introduce the concept of the maximal and the minimal Schmidt ranks for multipartite states. From the minimal Schmidt rank of the first order we present criterion of verifying unconditional robustness of genuine multipartite entanglement of multipartite pure states under superposition with product pure states. By the maximal Schmidt rank of the first order we verify the unconditional robustness of multipartite inseparability under superposition with product pure states. The number of product states superposed to a given entangled state which result in a separable state is investigated in detail. Furthermore the minimal Schmidt ranks of the second order are also introduced to identify the unconditional robustness of an entangled state for tripartite inseparability.