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.
tensor rank, border rank, algebraic complexity theory, quantum information theory
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)
Information (theme 2)
Simulations and Interfaces with Quantum Systems , Position-Based Quantum Cryptography
This work was funded by the The Netherlands Organisation for Scientific Research (NWO); grant id nwo/617.023.116 - Position-Based Quantum Cryptography
Algorithms and Complexity

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