Optical fibres with memory effects and their quantum communication capacities

If the transmissivity of an optical fibre falls below a critical value, its use as a reliable quantum channel is known to be drastically compromised. However, if the memoryless assumption does not hold – e.g. when input signals are separated by a sufficiently short time interval – the validity of this limitation is put into question. In this work we introduce a model of optical fibre that can describe memory effects for long transmission lines. We then solve its quantum capacity, two-way quantum capacity, and secret-key capacity exactly. By doing so, we show that – due to the memory cross-talk between the transmitted signals – reliable quantum communication is attainable even for highly noisy regimes where it was previously considered impossible.