Entanglement conditions for four-mode states via the uncertainty relations in conjunction with partial transposition

Abstract

From the Heisenberg uncertainty relation in conjunction with partial transposition, we derive a class of inequalities for detecting entanglements in four-mode states. The sufficient conditions for bipartite entangled states are presented. We also discuss the generalization of the entanglement conditions via the Schrödinger-Robertson indeterminacy relation, which are in general stronger than those based on the Heisenberg uncertainty relation. © Versita Warsaw and Springer-Verlag Berlin Heidelberg 2008.