  A class of two-qubit states called X-states are increasingly being used to
discuss entanglement and other quantum correlations in the field of quantum
information. Maximally entangled Bell states and "Werner" states are subsets of
them. Apart from being so named because their density matrix looks like the
letter X, there is not as yet any characterization of them. The su(2) X su(2) X
u(1) subalgebra of the full su(4) algebra of two qubits is pointed out as the
underlying invariance of this class of states. X-states are a seven-parameter
family associated with this subalgebra of seven operators. This recognition
provides a route to preparing such states and also a convenient algebraic
procedure for analytically calculating their properties. At the same time, it
points to other groups of seven-parameter states that, while not at first sight
appearing similar, are also invariant under the same subalgebra. And it opens
the way to analyzing invariant states of other subalgebras in bipartite
systems.
