  A protocol with the potential of beating the existing distance records for
conventional quantum key distribution (QKD) systems is proposed. It borrows
ideas from quantum repeaters by using memories in the middle of the link, and
that of measurement-device-independent QKD, which only requires optical source
equipment at the user's end. For certain fast memories, our scheme allows a
higher repetition rate than that of quantum repeaters, thereby requiring lower
coherence times. By accounting for various sources of nonideality, such as
memory decoherence, dark counts, misalignment errors, and background noise, as
well as timing issues with memories, we develop a mathematical framework within
which we can compare QKD systems with and without memories. In particular, we
show that with the state-of-the-art technology for quantum memories, it is
possible to devise memory-assisted QKD systems that, at certain distances of
practical interest, outperform current QKD implementations.
