Multipartite strongly symmetric states and applications to geometric entanglement and classicality

Multipartite quantum resources, such as entanglement and coherence, have long been a question of great interest in quantum information science. In this literature, we introduce the concept of multipartite strongly symmetric states that their representation tensors are strongly symmetric tensor. The dimension of strongly symmetric subspace is discussed, and show that is less than the dimension of symmetric subspace. We present some upper bound for the geometric measure of entanglement of strongly symmetric states, which are tighter than the bounds in N-qubit system. On the other hand, we consider the classicality of spin states in strongly symmetric situation, which is equivalent to the positive semidefiniteness of strongly symmetric representation tensor. Some sufficient conditions for classicality (separability) in strongly symmetric case are proposed, and these methods have a larger detection range than the smallest eigenvalue method. In addition, we also present some theoretical upper bounds for quantumness of strongly symmetric states, which are tighter than existing bounds.