  Entanglement is fundamental inasmuch because it rephrases the quest for the
classical-quantum demarcation line, and it also has potentially enormous
practical applications in modern information technology. In this work,
employing the approach of matrix decomposition, we introduce and formulate a
practicable criterion for separability based on the correlation tensor. It is
interesting that this criterion unifies several relevant separability criteria
proposed before, even stronger than some of them. Theoretical analysis and
detailed examples demonstrate its availability and feasibility for entanglement
detection. Furthermore we build a family of entanglement witnesses using the
criterion according to its linearity in the density operator space.
