Norm duality and the cross norm criteria for quantum entanglement

Abstract

We use duality techniques to prove and generalize the cross norm and computable cross norm criteria for separability of quantum states. While the original proof of the cross norm criterion is long and involved, our new proof is short and elementary. Furthermore, our proof generalizes naturally to arbitrary Schmidt number. We also use these techniques to generalize the computable cross norm criterion to arbitrary Schmidt number and prove some results of independent interest along the way.