Rotationally invariant bipartite states and bound entanglement

We consider rotationally invariant states in CN1⊗CN2CN1⊗CN2 Hilbert space with even N1⩾4N1⩾4 and arbitrary N2⩾N1N2⩾N1, and show that in such case there always exist states which are inseparable and remain positive after partial transposition, and thus the PPT criterion does not suffice to prove separability in such systems. We demonstrate it applying a map developed recently by Breuer [H.-P. Breuer, Phys. Rev. Lett. 97 (2006) 080501] to states that remain invariant after partial time reversal.