Memory-assisted measurement-device-independent quantum key distribution (MA-MDI-QKD) has recently been proposed as a possible intermediate step towards the realization of quantum repeaters. Despite its relaxing some of the requirements on quantum memories, the choice of memory in relation to the layout of the setup and the protocol has a stark effect on our ability to beat existing no-memory systems. Here, we investigate the suitability of nitrogen vacancy (NV) centers, as quantum memories, in MA-MDI-QKD. We particularly show that moderate cavity enhancement is required for NV centers if we want to outperform no-memory QKD systems. Using system parameters mostly achievable by today's state of the art, we then anticipate some total key rate advantage in the distance range between 300 and 500 km for cavity-enhanced NV centers. Our analysis accounts for major sources of error including the dark current, the channel loss, and the decoherence of the quantum memories.

Quantum memories are enabling devices for extending the reach of quantum key distribution (QKD) systems. The required specifications for memories are, however, often considered too demanding for available technologies. One can change this mindset by introducing memory-assisted measurement-deviceindependent QKD (MDI-QKD), which imposes less stringent conditions on the memory modules. It has been shown that, in the case of fast single-qubit memories, we can reach rates and distances not attainable by single no-memory QKD links. Single-qubit memories, such as single atoms or ions, have, currently, too slow of an access time to offer an advantage in practice. Here, we relax that assumption, and consider ensemble-based memories, which satisfy the main two requirements of having short access times and large storage-bandwidth products. Our results, however, suggest that the multiple-excitation effects in such memories can be so detrimental that they may wash away the scaling improvement offered by memory-equipped systems. We then propose an alternative setup that can in principle remedy the problem. As a prelude to our main problem, we also obtain secret key generation rates for MDI-QKD systems that rely on imperfect single-photon sources with nonzero probabilities of emitting two photons.Index Terms-Quantum cryptography, measurement-deviceindependent quantum key distribution, quantum memories.

The feasibility of trust-free long-haul quantum key distribution (QKD) is addressed. We combine measurement-device-independent QKD (MDI-QKD), as an access technology, with a quantum repeater setup, at the core of future quantum communication networks. This will provide a quantum link none of whose intermediary nodes need to be trusted, or, in our terminology, a trust-free QKD link. As the main figure of merit, we calculate the secret key generation rate when a particular probabilistic quantum repeater protocol is in use. We assume the users are equipped with imperfect single photon sources, which can possibly emit two single photons, or laser sources to implement decoy-state techniques. We consider apparatus imperfection, such as quantum efficiency and dark count of photodetectors, path loss of the channel, and writing and reading efficiencies of quantum memories. By optimizing different system parameters, we estimate the maximum distance over which users can share secret keys when a finite number of memories are employed in the repeater setup.

Quantum key distribution over probabilistic quantum repeaters is addressed. We compare, under practical assumptions, two such schemes in terms of their secret key generation rates per quantum memory. The two schemes under investigation are the one proposed by Duan et al. [Nature (London) 414, 413 (2001)]a n dt h a t of Sangouard et al. [ Phys. Rev. A 76, 050301 (2007)]. We consider various sources of imperfection in both protocols, such as nonzero double-photon probabilities at the sources, dark counts in detectors, and inefficiencies in the channel, photodetectors, and memories. We also consider memory decay and dephasing processes in our analysis. For the latter system, we determine the maximum value of the double-photon probability beyond which secret key distillation is not possible. We also find crossover distances for one nesting level to its subsequent one. We finally compare the two protocols in terms of their achievable secret key generation rates at their optimal settings. Our results specify regimes of operation where one system outperforms the other.