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Tensor Rank and Stochastic Entanglement Catalysis for Multipartite Pure States
The tensor rank (also known as generalized Schmidt rank) of multipartite pure states plays an important role in the study of entanglement classifications and transformations. We employ powerful tools from the theory of homogeneous polynomials to investigate the tensor rank of symmetric states such as the tripartite state $|{W}_{3}⟩=\frac{1}{\sqrt{3}}(|100⟩+|010⟩+|001⟩)$ and …