  We derive a general criterion to detect entangled states in multi-partite
systems based on the symmetric logarithmic derivative quantum Fisher
information. This criterion is a direct consequence of the fact that separable
states do not improve the accuracy upon estimating one-parameter family of
quantum channels. Our result is a generalization of the previously known
criterion for one-parameter unitary channel to any one-parameter quantum
channel. We discuss several examples to illustrate our criterion. The proposed
criterion is extended to the case of open quantum systems and we briefly
discuss how to detect entangled states in the presence of decoherence.
