Abstract
On the basis of linear programming, new sets of entanglement witnesses (EWs) for 3⊗3 and 4⊗4 systems are constructed. In both cases, the constructed EWs correspond to the hyper-planes contacting, without intersecting, the related feasible regions at line segments and restricted planes respectively. Due to the special property of the contacting area between the hyper-planes and the feasible regions, the corresponding hyper-planes can be turned around the contacting area throughout a bounded interval and hence create an infinite number of EWs. As these EWs are able to detect entanglement of some PPT states, they are non-decomposable (nd-EWs).
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