  We demonstrate that for every two-qubit state there is a X-counterpart, i.e.,
a corresponding two-qubit X-state of same spectrum and entanglement, as
measured by concurrence, negativity or relative entropy of entanglement. By
parametrizing the set of two-qubit X-states and a family of unitary
transformations that preserve the sparse structure of a two-qubit X-state
density matrix, we obtain the parametric form of a unitary transformation that
converts arbitrary two-qubit states into their X-counterparts. Moreover, we
provide a semi-analytic prescription on how to set the parameters of this
unitary transformation in order to preserve concurrence or negativity. We also
explicitly construct a set of X-state density matrices, parametrized by their
purity and concurrence, whose elements are in one-to-one correspondence with
the points of the concurrence versus purity (CP) diagram for generic two-qubit
states.
