Non-local properties of a symmetric two-qubit system

Non-local properties of symmetric two-qubit states are quantified in terms of a complete set of entanglement invariants. We prove that negative values of some of the invariants are signatures of quantum entanglement. This leads us to identify sufficient conditions for non-separability in terms of entanglement invariants. Non-local properties of two-qubit states extracted from (i) the Dicke state, (ii) a state generated by a one-axis twisting Hamiltonian, and (iii) a one-dimensional Ising chain with nearest neighbour interaction are analysed in terms of the invariants characterizing them.