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arXiv · 1705.07160

Theoretical and computational aspects of entanglement

Harm Derksen·Shmuel Friedland·Lek-Heng Lim·Li Wang
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Abstract

We show that the two notions of entanglement: the maximum of the geometric measure of entanglement and the maximum of the nuclear norm is attained for the same states. We affirm the conjecture of Higuchi-Sudberry on the maximum entangled state of four qubits. We introduce the notion of d-density tensor for mixed d-partite states. We show that d-density tensor is separable if and only if its nuclear norm is $1$. We suggest an alternating method for computing the nuclear norm of tensors. We apply the above results to symmetric tensors. We give many numerical examples.

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Harm Derksen, Shmuel Friedland, Lek-Heng Lim, Li Wang. 2017-05-19. Theoretical and computational aspects of entanglement. https://arxiv.org/abs/1705.07160

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