We propose a hybrid quantum repeater protocol combining the advantages of
continuous and discrete variables. The repeater is based on the previous work
of Brask et al. [Phys. Rev. Lett. 105, 160501 (2010)] but we present two ways
of improving this protocol. In the previous protocol entangled single-photon
states are produced and grown into superpositions of coherent states, known as
two-mode cat states. The entanglement is then distributed using homodyne
detection. To improve the protocol, we replace the time-consuming non-local
growth of cat states with local growth of single-mode cat states, eliminating
the need for classical communication during growth. Entanglement is generated
in subsequent connection processes. Furthermore the growth procedure is
optimized. We review the main elements of the original protocol and present the
two modifications. Finally the two protocols are compared and the modified
protocol is shown to perform significantly better than the original protocol.Comment: 14 pages, 7 figure