Entanglement of π -locally-maximally-entangleable states and the satisfiability problem

Adi Makmal, Markus Tiersch, Vedran Dunjko, Shengjun Wu

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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.

Original languageEnglish
Article number042308
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number4
StatePublished - 6 Oct 2014
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014 American Physical Society.


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