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.
Additional Metadata
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
Citation
Zuiddam, J. (2015). A note on the gap between rank and border rank.