Nonlocality of Symmetric States

In this paper we study the non-local properties of permutation symmetric states of n-qubits. We extend the bipartite Hardy paradox and the associated CH-inequality to n-party permutation symmetric states to show that all symmetric states exhibit non-locality. Natural extensions of both the paradoxes and the inequalities are developed which relate different entanglement classes to different non-local features. We define inequalities which are violated by all states of one entanglement class, whereas there are states outside that class which do not violate.