Nonclassicality witnesses and entanglement creation

Abstract

Several definitions of classicality are considered, such as P-representability, generalized coherent states and separable states. These notions are treated under a simple and general definition based on convex sets, which enables the use of the Hahn-Banach theorem to separate classical states from nonclassical ones. Nonclassicality linear witnesses are constructed, based on the observables available in a given physical situation. Some examples of nonclassical states are considered, with detection schemes available nowadays. Reviewing the concept of entanglement potential from a different perspective, it is shown that in some contexts an arbitrary single-system nonclassical state can be converted into a bipartite entangled state, provided a generalized controlled-displacement (e.g., beam-splitter, CNOT gate) is available. Also, this entanglement can be detected in a simple way using the nonclassicality witness of the original single-system state. Finally, we extend the discussion to multipartite states, proposing alternative ways to generate and classify multipartite entanglement.