A note on the gap between rank and border rank

Zuiddam, Jeroen

We study the tensor rank of a certain algebra. As a result we find a sequence of tensors with a large gap between rank and border rank, and thus a counterexample to a conjecture of Rhodes. We also obtain a new lower bound on the tensor rank of powers of the generalized W-state.

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Keywords	tensor rank, border rank, algebraic complexity theory, quantum information theory
MSC	Multilinear algebra, tensor products (msc 15A69), Computational aspects of associative rings (msc 16Z05), Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (msc 68Q17)
THEME	Information (theme 2)
Project	Simulations and Interfaces with Quantum Systems , Position-Based Quantum Cryptography
Grant	This work was funded by the The Netherlands Organisation for Scientific Research (NWO); grant id nwo/617.023.116 - Position-Based Quantum Cryptography
Organisation	Algorithms and Complexity
Citation APA Style AAA Style APA Style Cell Style Chicago Style Harvard Style IEEE Style MLA Style Nature Style Vancouver Style American-Institute-of-Physics Style Council-of-Science-Editors Style BibTex Format Endnote Format RIS Format CSL Format DOIs only Format	Zuiddam, J. (2015). A note on the gap between rank and border rank.

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