  Quantum entanglement lies at the heart of quantum mechanics and quantum
information processing. In this work, we show a new framework where entangled
states play the role of witnesses. We extend the notion of entanglement
witnesses, developing a hierarchy of witnesses for classes of observables. This
hierarchy captures the fact that entangled states act as witnesses for
detecting entanglement witnesses and separable states act as witnesses for the
set of non-block-positive Hermitian operators. Indeed, more hierarchies of
witnesses exist. We introduce the concept of \emph{finer} and \emph{optimal}
entangled states. These definitions not only give an unambiguous and
non-numeric quantification of entanglement and a new perspective on edge states
but also answer the open question of what the remainder of the best separable
approximation of a density matrix. Furthermore, we classify all entangled
states into disjoint families with optimal entangled states at its heart. This
implies that we can focus only on the study of a typical family with optimal
entangled states at its core when we investigate entangled states. Our
framework also assembles many seemingly different findings with simple
arguments that do not require lengthy calculations.
