Quantum key distribution over probabilistic quantum repeaters is addressed. We compare, under practical assumptions, two such schemes in terms of their secure key generation rate per memory, RQKD. The two schemes under investigation are the one proposed by Duan et al. in [Nat. 414, 413 (2001)] and that of Sangouard et al. proposed in [Phys. Rev. A 76, 050301 (2007)]. We consider various sources of imperfections in the latter protocol, such as a nonzero double-photon probability for the source, dark count per pulse, channel loss and inefficiencies in photodetectors and memories, to find the rate for different nesting levels. We determine the maximum value of the double-photon probability beyond which it is not possible to share a secret key anymore. We find the crossover distance for up to three nesting levels. We finally compare the two protocols.
Quantum key distribution over probabilistic quantum repeaters is addressed. We compare, under practical assumptions, two such schemes in terms of their secure key generation rate per memory, RQKD. The two schemes under investigation are the one proposed by Duan et al. in [Nat. 414, 413 (2001)] and that of Sangouard et al. proposed in [Phys. Rev. A 76, 050301 (2007)]. We consider various sources of imperfections in the latter protocol, such as a nonzero double-photon probability for the source, dark count per pulse, channel loss and inefficiencies in photodetectors and memories, to find the rate for different nesting levels. We determine the maximum value of the double-photon probability beyond which it is not possible to share a secret key anymore. We find the crossover distance for up to three nesting levels. We finally compare the two protocols.
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)] and that 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.
The feasibility of trust-free long-haul quantum key distribution (QKD) is addressed. We combine measurement-device-independent 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.
The feasibility of trust-free long-haul quantum key distribution (QKD) networks 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.
A feasible route toward implementing long-distance quantum key distribution (QKD) systems relies on probabilistic schemes for entanglement distribution and swapping as proposed in the work of Duan, Lukin, Cirac, and Zoller (DLCZ) [Nature (London) 414, 413 (2001)]. Here, we calculate the conditional throughput and fidelity of entanglement for DLCZ quantum repeaters by accounting for the DLCZ self-purification property in the presence of multiple excitations in the ensemble memories as well as loss and other sources of inefficiency in the channel and measurement modules. We then use our results to find the generation rate of secure key bits for QKD systems that rely on DLCZ quantum repeaters. We compare the key generation rate per logical memory employed in the two cases with and without a repeater node. We find the crossover distance beyond which the repeater system outperforms the nonrepeater one. That provides us with the optimum internode distancing in quantum repeater systems. We also find the optimal excitation probability at which the QKD rate peaks. Such an optimum probability, in most regimes of interest, is insensitive to the total distance.
Quantum key distribution (QKD) is one of the most prominent methods for secure exchange of cryptographic keys between two users. The laws of physics provide it with an immense tool \ntowards secure communications. Although QKD has been proven to reach distances on the order of a few hundreds of kilometers, the transmission rate of the key significantly drops when we go \nto further distances. One possible solution to this is to build a network of trusted nodes. The trust requirement will however narrow its scope of deployability. In this thesis, we focus on improving the key rate performance of secure communications by introducing imperfect quantum memories (QMs) in a measurement-device-independent (MDI) QKD system. \n \nIn this thesis, a protocol with the potential of beating the existing distance records for conventional QKD systems is proposed. It borrows ideas from quantum repeaters by using memories in the middle of the link, and that of MDI-QKD, which only requires optical source equipment at the user’s end. For certain fast memories, our scheme allows a higher repetition rate than that of quantum repeaters, 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 possible to devise memory-assisted QKD systems that, at certain distances of practical interest, outperform current QKD implementations. \n \nTo extend this work, we consider a suitable candidate that fullfils the requirements we have set for the QMs, i.e., the ensemble-based QMs. This type of memories, nevertheless, suffers from multiple-excitation effects, which can deteriorate the performance of the memory-assisted MDI-QKD system. As a solution we propose an alternative approach to the memory-assisted MDI-QKD by employing entangled-photon sources. We fully analyse this system by including modulation errors during the state-preparation at a single-photon source. We identify under which regimes of operation this system outperforms present QKD implementations. Overall we obtain a realistic account of what can be done with current technologies in order to improve the performance, in terms of rate versus distance, of QKD systems. Our findings can guide us toward implementing larger quantum networks.
We generalize measurement-device-independent quantum key distribution [Lo, Curty, and Qi, Phys. Rev. Lett. 108, 130503 (2012)] to the scenario where the Bell-state measurement station contains also heralded quantum memories. We find analytical formulas, in terms of device imperfections, for all quantities entering in the secret key rates, i.e., the quantum bit error rate and the repeater rate. We assume either single-photon sources or weak coherent pulse sources plus decoy states. We show that it is possible to significantly outperform the original proposal, even in presence of decoherence of the quantum memory. Our protocol may represent the first natural step for implementing a two-segment quantum repeater.