Constructing all entanglement witnesses from density matrices.

We demonstrate a general procedure to construct entanglement witnesses for any entangled state. This procedure is based on the trace inequality and a general form of entanglement witnesses, which is in the form W = ρ - cρI, where ρ is a density matrix, cρ is a non-negative number related to ρ, and I is the identity matrix. The general form of entanglement witnesses is deduced from Choi-Jamiolkowski isomorphism, that can be reinterpreted as that all quantum states can be obtained by a maximally quantum entangled state pass through certain completely positive maps. Furthermore, we provide the necessary and sufficient condition of the entanglement witness W = ρ - cρI in operation, as well as in theory. [ABSTRACT FROM AUTHOR]