Partial positive scaling transform: a separability criterion

Abstract

The problem of constructing a necessary and sufficient condition for establishing the separability of continuous variable systems is revisited. Simon [Phys. Rev. Lett. 84 (2000) 2726] pointed out that such a criterion may be constructed by drawing a parallel between the Peres' partial transpose criterion for finite-dimensional systems and partial time reversal transformation for continuous variable systems. We generalize the partial time reversal transformation to a partial scaling transformation and re-examine the problem using a tomographic description of the continuous variable quantum system. The limits of applicability of the entanglement criteria obtained from partial scaling and partial time reversal are explored.