TY - JOUR

T1 - Entanglement of π -locally-maximally-entangleable states and the satisfiability problem

AU - Makmal, Adi

AU - Tiersch, Markus

AU - Dunjko, Vedran

AU - Wu, Shengjun

N1 - Publisher Copyright:
© 2014 American Physical Society.

PY - 2014/10/6

Y1 - 2014/10/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84907921252&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.90.042308

DO - 10.1103/PhysRevA.90.042308

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AN - SCOPUS:84907921252

SN - 1050-2947

VL - 90

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 4

M1 - 042308

ER -