  Entanglement bits or ``ebits'' have been proposed as a quantitative measure
of a fundamental resource in quantum information processing. For such an
interpretation to be valid, it is important to show that the same number of
ebits in different forms or concentrations are inter-convertible in the
asymptotic limit. Here we draw attention to a very important but hitherto
unnoticed aspect of entanglement manipulation --- the classical communication
cost. We construct an explicit procedure which demonstrates that for bi-partite
pure states, in the asymptotic limit, entanglement can be concentrated or
diluted with vanishing classical communication cost. Entanglement of bi-partite
pure states is thus established as a truly inter-convertible resource.
