Universal methods for extending any entanglement witness from the bipartite to the multipartite case

Any bipartite entanglement witness $W$ can be written as $W=c_{sigma}I-sigma$, where $sigma$ is a quantum state, $I$ is the identity matrix, and $c_{sigma}$ is a non-negative number. We present a general method to extend the given entanglement witness to multipartite cases via purification, partial purification, and direct tensor of the quantum state $sigma$. Our methods extend $sigma$ but leave the parameter $c_{sigma}$ untouched. This is very valuable since the parameter is generally not easy to compute.