  We consider asymptotic convertibility of an arbitrary sequence of bipartite
pure states into another by local operations and classical communication
(LOCC). We adopt an information-spectrum approach to address cases where each
element of the sequences is not necessarily in tensor power of a bipartite pure
state. We derive necessary and sufficient conditions for the LOCC
convertibility of one sequence to another in terms of spectral entropy rates of
entanglement of the sequences. Based on these results, we also provide simple
proofs for previously known results on the optimal rates of entanglement
concentration and dilution of general sequences of pure states.
