Multipartite entanglement versus nonlocality for two families of N− qubit states

Entangled states of multiple qubits can violate Bell-type inequalities indicating nonlocal behavior of multiqubit quantum correlations. We analyze the relation between multipartite entanglement and genuine multipartite nonlocality, characterized by Svetlichny inequality violations, for two families of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>N</a:mi><a:mtext>−</a:mtext></a:mrow></a:math>qubit states. We show that for the generalized Greenberger-Horne-Zeilinger family of states, Svetlichny inequality is not violated when the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>n</b:mi><b:mtext>−</b:mtext></b:mrow></b:math>tangle is less than <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mn>1</c:mn><c:mo>/</c:mo><c:mn>2</c:mn></c:mrow></c:math> for any even number of qubits. On the other hand, the maximal slice states always violate the Svetlichny inequality when <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>n</d:mi><d:mtext>−</d:mtext></d:mrow></d:math>tangle is nonzero, and the violation increases monotonically with tangle. Our work generalizes the relations between tangle and Svetlichny inequality violations previously derived for three qubits.