Detecting multipartite classical states and their resemblances

We study various types of multipartite states lying near the quantum-classical boundary. The so-called classical states are precisely those in which each party can perfectly identify a locally held state without disturbing the global state, a task known as nondisruptive local state identification (NDLID). We show NDLID to be closely related local broadcasting, and we introduce a class of states called generalized classical states which allow for both NDLID and multipartite broadcasting when the most general quantum measurements are permitted. Simple analytical methods and a physical criterion are given for detecting whether a multipartite state is classical or generalized classical. For deciding the latter, a semidefinite programming algorithm is presented which may find use in other fields such as signal processing.