A note on the gap between rank and border rank
Commutative Algebra
2017-03-24 v2 Discrete Mathematics
Quantum Physics
Abstract
We study the tensor rank of the tensor corresponding to the algebra of n-variate complex polynomials modulo the dth power of each variable. 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. At the same time we obtain a new lower bound on the tensor rank of tensor powers of the generalised W-state tensor. In addition, we exactly determine the tensor rank of the tensor cube of the three-party W-state tensor, thus answering a question of Chen et al.
Keywords
Cite
@article{arxiv.1504.05597,
title = {A note on the gap between rank and border rank},
author = {Jeroen Zuiddam},
journal= {arXiv preprint arXiv:1504.05597},
year = {2017}
}
Comments
To appear in Linear Algebra and its Applications