Inseparability criteria for bipartite quantum states

E. Shchukin, W. Vogel

Published 2005-08-18, updated 2005-12-14Version 3

We provide necessary and sufficient conditions for the partial transposition of bipartite harmonic quantum states to be nonnegative. The conditions are formulated as an infinite series of inequalities for the moments of the state under study. The violation of any inequality of this series is a sufficient condition for entanglement. Previously known entanglement conditions are shown to be special cases of our approach.