  Quantum key distribution allows for the generation of a secret key between
distant parties connected by a quantum channel such as optical fibre or free
space. Unfortunately, the rate of generation of a secret key by direct
transmission is fundamentally limited by the distance. This limit can be
overcome by the implementation of so-called quantum repeaters. Here, we assess
the performance of a specific but very natural setup called a single sequential
repeater for quantum key distribution. We offer a fine-grained assessment of
the repeater by introducing a series of benchmarks. The benchmarks, which
should be surpassed to claim a working repeater, are based on finite-energy
considerations, thermal noise and the losses in the setup. In order to boost
the performance of the studied repeaters we introduce two methods. The first
one corresponds to the concept of a cut-off, which reduces the effect of
decoherence during storage of a quantum state by introducing a maximum storage
time. Secondly, we supplement the standard classical post-processing with an
advantage distillation procedure. Using these methods, we find realistic
parameters for which it is possible to achieve rates greater than each of the
benchmarks, guiding the way towards implementing quantum repeaters.
