  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.
