CONSTRUCTION OF A FAMILY OF POSITIVE BUT NOT COMPLETELY POSITIVE MAP FOR THE DETECTON OF ENTANGLED STATES

Abstract

We have constructed a family of map. The map is shown to be positive when imposing certain condition on the parameters. Then we show that the constructed map can never be completely positive. After tuning the parameters, we found that the map still remain positive but it is not completely positive. We then use the positive but not completely positive map in the detection of entanglement of a composite bipartite quantum system such as Bound Entangled States (BES) and Negative Partial Transpose Entangled States (NPTES)