  In the absence of quantum repeaters, quantum communication proved to be
nearly impossible across optical fibres longer than $\gtrsim 20\text{ km}$ due
to the drop of transmissivity below the critical threshold of $1/2$. However,
if the signals fed into the fibre are separated by a sufficiently short time
interval, memory effects must be taken into account. In this paper we show that
by properly accounting for these effects it is possible to devise schemes that
enable unassisted quantum communication across arbitrarily long optical fibres
at a fixed positive qubit transmission rate. We also demonstrate how to achieve
entanglement-assisted communication over arbitrarily long distances at a rate
of the same order of the maximum achievable in the unassisted noiseless case.
