Theoretical and computational aspects of entanglement

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.

arXiv comment34 pages, 12 tables

References in corpus (10)

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• A Schmidt number for density matrices
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Cited by in corpus (5)

• On decompositions and approximations of conjugate partial-symmetric complex tensors
• Spectral inequalities for nonnegative tensors and their tropical analogues
• Separability of Hermitian Tensors and PSD Decompositions
• Hermitian Tensor Decompositions
• On orthogonal tensors and best rank-one approximation ratio