Quantum repeaters based on entanglement purification

We study the use of entanglement purification for quantum communication ove r long distances. For distances much longer than the coherence length of a corresponding noisy quantum channel, the fidelity of transmission is usuall y so low that standard purification methods are not applicable. It is possi ble, however, to divide the channel into shorter segments that are purified separately and then connected by the method of entanglement swapping. This method can be much more efficient than schemes based on quantum error corr ection, as it makes explicit use of two-way classical communication. An imp ortant question is how the noise, introduced by imperfect local operations (that constitute-the protocols of purification and the entanglement swappin g), accumulates in such a compound channel, and how it can be kept below a certain noise level: To treat this problem, we first study the applicabilit y and the efficiency of entanglement purification protocols in the situatio n of imperfect local operations. We then present a scheme that allows entan glement purification over arbitrary long channels and tolerates errors on t he percent level. It requires a polynomial overhead in time, and an overhea d in local resources that grows only logarithmically - with the length of t he-channel. [S1050-2947(99)09801-7].