A Family of Bipartite Separability Criteria Based on Bloch Representation of Density Matrices

We study the separability of bipartite quantum systems in arbitrary dimensions based on the Bloch representation of density matrices. We present two separability criteria for quantum states in terms of the matrices $T_{\alpha \beta }(\rho )$ and $W_{ab,\alpha \beta }(\rho )$ constructed from the correlation tensors in the Bloch representation. These separability criteria can be simplified and detect more entanglement than the previous separability criteria. Detailed examples are given to illustrate the advantages of results.