  Entanglement distribution between distant parties is an essential component
to most quantum communication protocols. Unfortunately, decoherence effects
such as phase noise in optical fibers are known to demolish entanglement.
Iterative (multistep) entanglement distillation protocols have long been
proposed to overcome decoherence, but their probabilistic nature makes them
inefficient since the success probability decays exponentially with the number
of steps. Quantum memories have been contemplated to make entanglement
distillation practical, but suitable quantum memories are not realised to date.
Here, we present the theory for an efficient iterative entanglement
distillation protocol without quantum memories and provide a proof-of-principle
experimental demonstration. The scheme is applied to phase-diffused
two-mode-squeezed states and proven to distill entanglement for up to three
iteration steps. The data are indistinguishable from those an efficient scheme
using quantum memories would produce. Since our protocol includes the final
measurement it is particularly promising for enhancing continuous-variable
quantum key distribution.
