  Strong numerical evidence is presented suggesting that all two-qubit mixed
states are equivalent to X states by a single entanglement-preserving unitary
(EPU) transformation, so that the concurrence of such an X state equals that of
the original general state. An X-state parameterization of a general two-qubit
state is given, allowing all states to have their concurrence parametrically
specified. A new kind of entanglement measure is proposed, relating a general
state's entanglement to that of a pure state in the same system. New states
called "H States" are presented, having fully parametric concurrence and
purity, with the intention of using them to construct entanglement-preserving
depolarization channels, which may aid development of the new entanglement
measure. A theory of "true-generalized" X states (TGX states) is proposed for
the general case of $N$-partite systems. While such states do not generally
have the literal "X" shape, evidence is shown that they are the true
generalizations of X states in larger systems, since they appear to always be
EPU-equivalent to general states of all ranks, whereas literal X states
generally are not. An example of this is given for $2\times 3$, including the
proposition of the $2\times 3$ maximally entangled mixed states (MEMS). If the
claim that TGX states are universal is valid, then any entanglement measure may
be computable in a simpler form by using the EPU-equivalence between general
states and TGX states.
