Entanglement condition using Schrodinger-Robertson uncertainty relation

Compared with the Heisenberg uncertainty relation, Schrodinger-Robertson uncertain relation generally provides stronger bound on product of uncertainties for two noncommutation observables, so the stricter separability condition can be provided by using Schrodinger-Robertson uncertainty relation. In this paper, using the Schrodinger Robertson uncertainty relation, the separability condition previously proposed by L. M. Duan is improved into the stricter separability condition. Then we extend the above ideas to the general two-mode situation and multi-mode terms, some new separation conditions are obtained.