Rotationally invariant bipartite states and bound entanglement

Abstract

We consider rotationally invariant states in $\mathbb{C}^{N_{1}}\ot \mathbb{C}^{N_{2}}$ Hilbert space with even $N_{1}\geq 4$ and arbitrary $N_{2}\geq N_{1}$, 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 of such systems. We demonstrate it applying a map developed recently by Breuer [H.-P. Breuer, Phys. Rev. Lett {\bf 97}, 080501 (2006)] to states that remain invariant after partial time reversal.