Entanglement Witness $2.0$: Compressed/Mirrored Entanglement Witnesses

Abstract: An entanglement witness is an observable detecting entanglement for a subset of states. We present a framework that makes an entanglement witness twice as powerful due to the general existence of a second (lower) bound, in addition to the (upper) bound of the very definition. This second bound, if non-trivial, is violated by another subset of entangled states. Differently stated, we prove via the structural physical approximation that two witnesses can be compressed into a single one. Consequently, our framework shows that any entanglement witness can be upgraded to a witness $2.0$. The generality and its power are demonstrate by applications to bipartite and multipartite qubit/qudit systems.