In this paper we investigate the entanglement properties of the class of π-locally-maximally-entangleable (π-LME) states, which are also known as the real equally weighted states or the hypergraph states. The π-LME states comprise well-studied classes of quantum states (e.g., graph states) and exhibit a large degree of symmetry. Motivated by the structure of LME states, we show that the capacity to (efficiently) determine if a π-LME state is entangled would imply an efficient solution to the Boolean satisfiability problem. More concretely, we show that this particular problem of entanglement detection, phrased as a decision problem, is NP-complete. The restricted setting we consider yields a technically uninvolved proof, and illustrates that entanglement detection, even when quantum states under consideration are highly restricted, still remains difficult.
|Journal||Physical Review A - Atomic, Molecular, and Optical Physics|
|State||Published - 6 Oct 2014|
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© 2014 American Physical Society.