Long-distance quantum key distribution with imperfect devices

Quantum key distribution (QKD) is one of the most promising techniques for the secure exchange of cryptographic keys between two users. Its unique property of relying on the laws of physics makes it an appealing tool for secure communications. While QKD has been implemented over distances on the order of a few hundreds of kilometers, the transmission rate of the key severely drops, when we go to further distances. An easy solution to this could rely on a network of trusted nodes. This solution, however, is far from ideal. In this thesis, we focus on obtaining long-distance secure communications by using trust-free intermediate nodes between two users. Quantum repeaters will then be at the core of our work and we analytically study different systems under realistic scenarios. We cover a range of repeater setups incorporating quantum memories (QMs), in terms of their short-term and long-term feasibility and in terms of ease of access for end users. We consider the main imperfections of the employed devices. In particular, we consider ensemble-based QMs, which offer a feasible route toward the implementation of probabilistic quantum repeaters. We study the effects of multiple excitations in such QMs and its effects on the key rate in a memory-assisted measurement device- independent QKD (MDI-QKD) system. We then analytically compare the performance of two probabilistic quantum repeater protocols by calculating their secure key rates. We identify under which regimes of operation one system outperforms the other. Source and memory imperfections are considered in our analysis. Finally, we combine a quantum repeater scheme with the MDI-QKD protocol and we derive the largest distances that is possible to reach under practical assumptions. Overall we obtain a realistic account of what can be done with existing technologies in order to improve the reach and the rate of QKD systems within a larger quantum network.