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

中文翻译：

---

纠缠对称态和共正矩阵

对称量子态中的纠缠和同正矩阵理论是密切相关的概念。对于最简单的对称状态，即对角对称 (DS) 状态，已经表明异常（非异常）共正矩阵和不可分解（可分解）纠缠见证 (EW) 之间存在对应关系。在这里，我们展示了对称状态的 EW，但不是 DS，状态也可以从扩展的共正矩阵构造，提供了任意奇维中的束缚纠缠对称状态及其相应 EW 的新示例。