Local implementation of witness operators for entanglement detection

Several results on local decompositions of witnesses for different situations are presented. Witnesses detecting NPT states in bipartite systems of N /spl times/ M dimensions are considered and bounds on the minimal number of needed local measurements are given. In this way some of decompositions are proved to be optimal. Similar analysis is performed for bound entangled states in 2 /spl times/ 4 and 3 /spl times/ 3 dimensions. Also for three- and four-qubit states, witnesses can be constructed that allow to distinguish between different entanglement classes.