Quantum entanglement nowadays plays a fundadamental role in Quantum Optics and Quantum Information Theory. Entanglement is a nonclassical correlation between the parties of a compound quantum system. This kind of correlations cannot be described by a classical joint probability distribution between the subsytems. In this work, we present new approaches for the identification, representation by quasi-probabilities, and quantification of entanglement.
For the identification and the representation by quasi-probabilities we have derrived separability eigenvalue equations. From the solution of these equations we obtain all observables witnessing the entanglement of a state. On the other hand, the solution also yields an optimized quasi-probability distribution of entanglement. The negativities of this distribution allow us to conclude that no classical probability can generate the considerd state in terms of factorizeable ones. For the quantification of entanglement we compare well-known entanglement measures. We conclude that the Schmidt number - the number of global superpositions - has advantageous properties compared to measures based on a distance.
We generalize our method to so-called Schmidt number states and multipartite entangled states. We relate our findings to the notion of nonclassicality of radiation fields. Moreover, we transfer our new methods to this notion.