  We present an explicit family of two-qubit X states with
entanglement-preserving unitary (EPU) equivalence to the set of general states;
that is, for any spectrum-entanglement combination achievable by general
states, this family contains an X state of the same spectrum and entanglement.
This idea was originally conjectured by the author and supported with strong
numerical evidence in arXiv:1310.7038. Then, in Ann. Phys. 351 (2014) 79, the
authors proved the existence of such two-qubit unitary transformations, but
found the parameters to be transcendental, eluding explicit solution. Here, by
a different method, we prove the existence of such transformations, obtain a
compact implicit solution for them, and provide an exact, explicit form of the
desired X-state family.
