Abstract
State space structure of tripartite quantum systems is analyzed. In particular, it has been shown that the set of states separable across all the three bipartitions [say B^int(ABC)] is a strict subset of the set of states having positive partial transposition (PPT) across the three bipartite cuts [say P^int(ABC)] for all the tripartite Hilbert spaces C_A^d₁⊗C_B^d₂⊗C_C^d₃ with min{d₁,d₂,d₃}≥2. The claim is proved by constructing state belonging to the set P^int(ABC) but not belonging to B^int(ABC). For (C^d)^⊗3 with d≥3, the construction follows from specific type of multipartite unextendible product bases. However, such a construction is not possible for (C²)^⊗3 since for any n the bipartite system C²⊗Cⁿ cannot have any unextendible product bases [Phys. Rev. Lett. 82, 5385 (1999)]. For the 3-qubit system we, therefore, come up with a different construction.