1. Highly entangled tensors.
- Author
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Derksen, Harm and Makam, Visu
- Subjects
- *
MEASUREMENT - Abstract
A geometric measure for the entanglement of a unit length tensor T ∈ (C n ) ⊗ k is given by − 2 log 2 ∥ T ∥ σ , where ∥ ⋅ ∥ σ denotes the spectral norm. A simple induction gives an upper bound of (k − 1) log 2 (n) for the entanglement. We show the existence of tensors with entanglement larger than k log 2 (n) − log 2 (k) − o (log 2 (k)). Friedland and Kemp (Proc. AMS, 2018) have similar results in the case of symmetric tensors. Our techniques give improvements in this case. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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