It is shown that every entangled state in an infinite-dimensional composite system has a simple entanglement witness of the form $\alpha I+T$ with $\alpha$ a non-negative number and $T$ a finite rank self-adjoint operator. We also provide two methods of constructing an entanglement witness and apply them to obtain some entangled states that cannot be detected by the positive partial transpose criterion and the realignment criterion.

• Received 10 April 2010

DOI:https://doi.org/10.1103/PhysRevA.81.062351