Further results on the cross norm criterion for separability

In the present paper we develop and investigate a novel approach that aims to characterize quantum entanglement by using cross norms. In the first part of the paper we further develop the mathematical theory by determining the value of the greatest cross norm for Werner states, for isotropic states and for Bell diagonal states. In the second part we show that our techniques induce a novel powerful analytical and computable separability criterion for bipartite systems. This new criterion complements the well-known Peres positive partial transpose criterion in several aspects. It is a necessary but in general not a sufficient criterion for separability We demonstrate the power of the new criterion by evaluating the criterion for a number of important examples. We also demonstrate that the new criterion is able to detect bound entangled states.