Chiral symmetric three-particle subspaces are maximally entangled, yield U⊗3-invariant entanglement witnesses, and lead to a simple SDP solution for genuine multipartite entanglement in unitarily invariant states.
Theoretical and computational aspects of entanglement
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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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Chiral Symmetries and Multiparticle Entanglement
Chiral symmetric three-particle subspaces are maximally entangled, yield U⊗3-invariant entanglement witnesses, and lead to a simple SDP solution for genuine multipartite entanglement in unitarily invariant states.