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.
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.
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.
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.
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.
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.
We analyze various prominent quantum repeater protocols in the context of long-distance quantum key distribution. These protocols are the original quantum repeater proposal by Briegel, D\"ur, Cirac and Zoller, the so-called hybrid quantum repeater using optical coherent states dispersively interacting with atomic spin qubits, and the Duan-Lukin-Cirac-Zoller-type repeater using atomic ensembles together with linear optics and, in its most recent extension, heralded qubit amplifiers. For our analysis, we investigate the most important experimental parameters of every repeater component and find their minimally required values for obtaining a nonzero secret key. Additionally, we examine in detail the impact of device imperfections on the final secret key rate and on the optimal number of rounds of distillation when the entangled states are purified right after their initial distribution.
We present an exact rate analysis for a secret key that can be shared among two parties employing a linear quantum repeater chain. One of our main motivations is to address the question whether simply placing quantum memories along a quantum communication channel can be beneficial in a realistic setting. The underlying model assumes deterministic entanglement swapping of single-spin quantum memories and it excludes probabilistic entanglement distillation, and thus two-way classical communication, on higher nesting levels. Within this framework, we identify the essential properties of any optimal repeater scheme: entanglement distribution in parallel, entanglement swapping as soon and parallel quantum storage as little as possible. While these features are obvious or trivial for the simplest repeater with one middle station, for more stations they cannot always be combined. We propose an optimal scheme including channel loss and memory dephasing, proving its optimality for the case of two stations and conjecturing it for the general case. In an even more realistic setting, we consider additional tools and parameters such as memory cutoffs, multiplexing, initial state and swapping gate fidelities, and finite link coupling efficiencies in order to identify potential regimes in memory-assisted quantum key distribution beyond one middle station that exceed the rates of the smallest quantum repeaters as well as those obtainable in all-optical schemes unassisted by stationary memory qubits and two-way classical communication. Our analytical treatment enables us to determine simultaneous trade-offs between various parameters, their scaling, and their influence on the performance ordering among different types of protocols, comparing two-photon interference after dual-rail qubit transmission with one-photon interference of single-rail qubits or, similarly, optical interference of coherent states. We find that for experimental parameter values that are highly demanding but not impossible (up to 10 s coherence time, about 80% link coupling, and state or gate infidelities in the regime of 1%--2%), one secret bit can be shared per second at a total channel loss budget of 157.6 dB, i.e. a total distance of 800 km for a fiber attenuation length of 22 km with repeater stations placed at every 100 km---a clear improvement over realistic twin-field or, much more pronouncedly, ideal point-to-point quantum key distribution at GHz clock rates.