Classical Communication Cost of Entanglement Manipulation: Is Entanglement an Interconvertible Resource?

Entanglement bits or ``ebits'' have been proposed as a quantitative measure of a fundamental resource in quantum information processing. It is, thus, important to show that the same number of ebits in different forms are interconvertible 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 bipartite pure states, in the asymptotic limit, entanglement can be concentrated or diluted with vanishing classical communication cost. Entanglement of bipartite pure states is thus established as a truly interconvertible resource.