  Entanglement of pure states of bipartite quantum systems has been shown to
have a unique measure in terms of the von Neumann entropy of the reduced states
of either of its subsystems. The measure is established under entanglement
manipulation of an asymptotically large number of copies of the states. In this
paper, different asymptotic measures of entanglement assigned to arbitrary
sequences of bipartite pure states are shown to coincide only when the sequence
is information stable, in terms of the quantum spectral information rates of
the sequence of subsystem states. Additional bounds on the optimal rates of
entanglement manipulation protocols in quantum information are also presented,
including bounds given by generalizations of the coherent information and the
relative entropy of entanglement.
