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The problem of bound entanglement detection is a challenging aspect ofquantum information theory for higher dimensional systems. Here, we propose anindecomposable positive map for two-qutrit systems, which is shown to generatea class of positive partial transposed (PPT) states. A corresponding witnessoperator is constructed and shown to be weakly optimal and locallyimplementable. Further, we perform a structural physical approximation of theindecomposable map to make it a completely positive one, and find a new PPTentangled state which is not detectable by certain other well-knownentanglement detection criteria.

Generating and detecting bound entanglement in two-qutrits using a family of indecomposable positive maps