Constructing entanglement witnesses for infinite-dimensional systems

Abstract

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 nonnegative number and $T$ a finite rank self-adjoint operator. We also provide two methods of constructing entanglement witness and apply them to obtain some entangled states that cannot be detected by the PPT criterion and the realignment criterion.

15 pages

References in corpus (2)

• Detecting Genuine Multipartite Entanglement with Two Local Measurements
• Necessary and sufficient conditions for bipartite entanglement

Cited by in corpus (4)

• A characterization of positive linear maps and criteria of entanglement for quantum states
• Positive finite rank elementary operators and characterizing entanglement of states
• When different entanglement witnesses detect entangled states simultaneously
• The RCCN criterion of separability for states in infinite-dimensional quantum systems