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