Entanglement and collective quantum operations

We show how shared entanglement, together with classical communication and local quantum operations, can be used to perform an arbitrary collective qu antum operation upon N spatially-separated qubits. A simple teleportation-b ased protocol for achieving this, which requires 2(N - 1) ebits of shared, bipartite entanglement and 4(N - 1) classical bits, is proposed. In terms o f the total required entanglement, this protocol is shown to be optimal for even N in both the asymptotic Limit and for 'one-shot' applications. (C) 2 000 Published by Elsevier Science B.V.