Entangled symmetric states and copositive matrices

Entanglement in symmetric quantum states and the theory of copositive matrices are intimately related concepts. For simplest states, i.e., diagonal (DS) it has been shown that there exists a correspondence between exceptional (non-exceptional) non-decomposable (decomposable) Witnesses (EWs). Here we show EWs symmetric, but not DS, can also be constructed from extended matrices, providing new examples bound entangled together with their corresponding EWs, arbitrary odd dimensions.