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.