Tensor rank and stochastic entanglement catalysis for multipartite pure states

Lin Chen, Eric Chitambar, Runyao Duan, Zhengfeng Ji, Andreas Winter

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Abstract

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 |W3=1√3(|100+|010+|001) and its N-partite generalization |WN. Previous tensor rank estimates are dramatically improved and we show that (i) three copies of |W3 have a rank of either 15 or 16, (ii) two copies of |WN have a rank of 3N-2, and (iii) n copies of |WN have a rank of O(N). A remarkable consequence of these results is that certain multipartite transformations, impossible even probabilistically, can become possible when performed in multiple-copy bunches or when assisted by some catalyzing state. This effect is impossible for bipartite pure states.

Original languageEnglish
Article number200501
JournalPhysical Review Letters
Volume105
Issue number20
DOIs
StatePublished - 8 Nov 2010
Externally publishedYes

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