Quantum repeaters based on entanglement purification

TLDR

Long‑distance quantum channels exceed the coherence length, yielding such low fidelity that conventional purification fails. The authors investigate how imperfect local operations affect noise accumulation in entanglement purification and propose a scheme that tolerates percent‑level errors over arbitrarily long channels. They divide the channel into short segments, purify each with entanglement purification, connect them via entanglement swapping, achieving polynomial time overhead and logarithmic resource growth. This approach outperforms quantum‑error‑correction schemes by exploiting two‑way classical communication and tolerates errors at the percent level.

Abstract

We study the use of entanglement purification for quantum communication over long distances. For distances much longer than the coherence length of a corresponding noisy quantum channel, the fidelity of transmission is usually so low that standard purification methods are not applicable. It is possible, 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 correction, as it makes explicit use of two-way classical communication. An important question is how the noise, introduced by imperfect local operations (that constitute the protocols of purification and the entanglement swapping), 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 applicability and the efficiency of entanglement purification protocols in the situation of imperfect local operations. We then present a scheme that allows entanglement purification over arbitrary long channels and tolerates errors on the percent level. It requires a polynomial overhead in time, and an overhead in local resources that grows only logarithmically with the length of the channel.