Suppose I have an $n$ -qubit pure state $|\psi\rangle$ that I can prepare using a unitary $U$ s.t. $U|0\rangle = |\psi\rangle$ . I would like to determine whether the first qubit in the system is unentangled from the rest. The other registers may have some nontrivial entanglement with each other, but I'm not interested in that. I was wondering if there are any references that have looked at this problem (or perhaps a weaker formulation of it, though I'm not sure how a weaker formulation would be