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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., Comment: 19 pages, 2 figures. The full technical details, proofs and additional developments are deferred to the companion paper [F. A. Mele, L. Lami, and V. Giovannetti. Quantum optical communication in the presence of strong attenuation noise. Preprint arXiv:2204.13129, 2022]. In v3 minor typos have been fixed

Is quantum communication possible over an optical fibre with transmissivity $\lambda\leq 1/2$ ? The answer is well known to be negative if the environment with which the incoming signal interacts is initialised in a thermal state. However, in [PRL 125:110504, 2020] the quantum capacity was found to be always bounded away from zero for all $\lambda>0$, a phenomenon dubbed "die-hard quantum communication" (D-HQCOM), provided that the initial environment state can be chosen appropriately (depending on $\lambda$). Here we show an even stronger version of D-HQCOM in the context of entanglement-assisted classical communication: entanglement assistance and control of the environment enable communication with performance at least equal to that of the ideal case of absence of noise, even if $\lambda>0$ is arbitrarily small. These two phenomena of D-HQCOM have technological potential provided that we are able to control the environment. How can we achieve this? Our second main result answers this question. Here we provide a fully consistent protocol to activate the phenomena of D-HQCOM without directly accessing the environment state. This is done by sending over the channel "trigger signals", i.e. signals which do not encode information, prior to the actual communication, with the goal of modifying the environment in an advantageous way. This is possible thanks to the memory effects which arise when the sender feeds signals separated by a sufficiently short temporal interval. Our results may offer a concrete scheme to communicate across arbitrarily long optical fibres, without using quantum repeaters. As a by-product of our analysis, we derive a simple Kraus representation of the thermal attenuator exploiting the associated Lindblad master equation., Comment: 38 pages, 12 figures. The present paper serves as the companion to the paper [F. A. Mele, L. Lami, and V. Giovannetti. Restoring quantum communication efficiency over high loss optical fibres. Preprint arXiv:2204.13128, 2022], by providing proofs of the results stated there and additional developments. In v3 minor typos have been fixed