  Quantum information science has profoundly changed the ways we understand,
store, and process information. A major challenge in this field is to look for
an efficient means for classifying quantum state. For instance, one may want to
determine if a given quantum state is entangled or not. However, the process of
a complete characterization of quantum states, known as quantum state
tomography, is a resource-consuming operation in general. An attractive
proposal would be the use of Bell's inequalities as an entanglement witness,
where only partial information of the quantum state is needed. The problem is
that entanglement is necessary but not sufficient for violating Bell's
inequalities, making it an unreliable state classifier. Here we aim at solving
this problem by the methods of machine learning. More precisely, given a family
of quantum states, we randomly picked a subset of it to construct a
quantum-state classifier, accepting only partial information of each quantum
state. Our results indicated that these transformed Bell-type inequalities can
perform significantly better than the original Bell's inequalities in
classifying entangled states. We further extended our analysis to three-qubit
and four-qubit systems, performing classification of quantum states into
multiple species. These results demonstrate how the tools in machine learning
can be applied to solving problems in quantum information science.
