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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Simulations and Interfaces with Quantum Systems , Position-Based Quantum Cryptography
Algorithms and Complexity

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