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We introduce systematically with the help of Weyl operators novel classes ofmultipartite and multidimensional states which are all bound entangled forarbitrary dimension. We find that the entanglement is bound due to differentreasons: unlockable due to the multi--particle nature and some states are inaddition bound due the fact being positive under partial transposition (PPT).By a general construction (W simplices) we obtain classes of states which havethe same geometry concerning separability and entanglement independent of thenumber of involved particle pairs. Moreover, we introduce a distillationprotocol and demonstrate for d=3 that for a certain set of states theentanglement can be increased only up to a certain amount.

Two distinct classes of bound entanglement: PPT-bound and `multi-particle'-bound