Entanglement Concentration is Irreversible

In quantum information theory, it is widely believed that entanglement concentration for bipartite pure states is asymptotically reversible. In order to examine this, we give a precise formulation of the problem, and show a trade-off relation between performance and reversibility, which implies the irreversibility of entanglement concentration. Then, we regard entanglement concentration as entangled state compression in an entanglement storage with lower dimension. Because of the irreversibility of entanglement concentration, an initial state cannot be completely recovered after the compression process and a loss inevitably arises in the process. We numerically calculate this loss and also derive for it a highly accurate analytical approximation.