A protocol with the potential of beating the existing distance records for conventional quantum key distribution (QKD) systems is proposed. It borrows ideas from quantum repeaters by using memories in the middle of the link, and that of measurement-device-independent QKD, which only requires optical source equipment at the userʼs end. For certain memories with short access times, our scheme allows a higher repetition rate than that of quantum repeaters with single-mode memories, thereby requiring lower coherence times. By accounting for various sources of nonideality, such as memory decoherence, dark counts, misalignment errors, and background noise, as well as timing issues with memories, we develop a mathematical framework within which we can compare QKD systems with and without memories. In particular, we show that with the state-of-the-art technology for quantum memories, it is potentially possible to devise memory-assisted QKD systems that, at certain distances of practical interest, outperform current QKD implementations.Keywords: quantum key distribution, quantum memory, measurement device independent, quantum repeaters, quantum networks IntroductionDespite all commercial [1] and experimental achievements in quantum key distribution (QKD) [2-10], reaching arbitrarily long distances is still a remote objective. The fundamental solution to this problem, i.e., quantum repeaters, has been known for over a decade. From early proposals by Briegel et al [11] to the latest no-memory versions [12][13][14], quantum repeaters, typically, rely on highly efficient quantum gates comparable to what we may need for future quantum computers. While the progress on that ground may take some time before such systems become functional, another approach based on probabilistic gate operations was proposed by Duan and co-workers [15], which could offer a simpler way of implementing quantum repeaters for moderate distances of up to around 1000 km. The latter systems require quantum memory (QM) modules with high coupling efficiencies to light and with coherence times exceeding the transmission delays, which are yet to be achieved together. In this paper, we propose a protocol that, although is not as scalable as quantum repeaters, for certain classes of memories, relaxes, to some extent, the harsh requirements on memories' coherence times, thereby paving the way for the existing technologies to beat the highest distance records achieved for no-memory QKD links [2]. The idea behind our protocol was presented in [16], and independent work has also been reported in [17]. This work proposes additional practical schemes and rigorously analyses them under realistic conditions. Our protocol relies on concepts from quantum repeaters, on the one hand, and the recently proposed measurement-device-independent QKD (MDI-QKD), on the other. The original MDI-QKD [18] relies on sending encoded photons by the users to a middle site at which a Bell-state measurement (BSM) is performed. One major practical advantage of MDI-QKD is that this BSM can be...

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.

Abstract-Three network architectures, compatible with passive optical networks, for future hybrid quantum-classical networks are proposed and compared. These setups rely on three different schemes for quantum key distribution (QKD): BB84, entanglement-based QKD, and measurement-device-independent QKD (MDI-QKD). It turns out that, while for small-to-moderatesize networks BB84 supports the highest secret key generation rate, it may fail to support large numbers of users. Its cost implications are also expected to be higher than other setups. For large networks, MDI-QKD offers the highest key rate if fast single-photon detectors are employed. Entanglement-based networks offer the longest security distance among the three setups. MDI-QKD is, however, the only architecture resilient to detection loopholes and possibly the most favorable with its less demanding end-user technology. Entanglement-based and MDI-QKD setups can both be combined with quantum repeater systems to allow for long-distance QKD with no trust constraints on the service provider.

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