Computable Cross-norm Criterion for Separability

Oliver Rudolph

Oliver Rudolph

The computable cross-norm (CCN) criterion is a powerful analytical and computable separability criterion for bipartite quantum states, which is also known to systematically detect bound entanglement. In certain aspects this criterion complements the well-known Peres positive partial transpose (PPT) criterion. In the present paper we study important analytical properties of the CCN criterion. We show that in contrast to the PPT criterion it is not sufficient in dimension $2\ifmmode\times\else\texttimes\fi{}2.$ In higher dimensions, theorems connecting the fidelity of a quantum state with the CCN criterion are proved. We also analyze the behavior of the CCN criterion under local operations and identify the operations that leave it invariant. It turns out that the CCN criterion is in general not invariant under local operations.

Oliver Rudolph

Otfried Gühne, Matyas I. Mechler, Géza Tóth +1 more

We show that any state that violates the computable cross norm (or realignment) criterion for separability also violates the separability criterion of the local uncertainty relations. The converse is not true. The local uncertainty relations provide a straightforward construction of nonlinear entanglement witnesses for the cross norm criterion.

Oliver Rudolph

The computable cross norm (CCN) criterion for separability is neither weaker nor stronger than the positive partial transpose (PPT) criterion.

David Pérez-Garcı́a