  The computable cross norm (CCN) criterion is a new powerful analytical and
computable separability criterion for bipartite quantum states, that 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 x 2. In higher dimensions we prove theorems
connecting the fidelity of a quantum state with the CCN criterion. We also
analyze the behaviour 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.
