Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1208.2201 · Physical Review A

Quantum repeaters and quantum key distribution: Analysis of secret-key rates

Silvestre Abruzzo, Sylvia Bratzik, Nadja K. Bernardes, Hermann Kampermann, Peter van Loock, Dagmar Bruß

Published May 17, 2013• 61 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.87.052315

Related papers

Secret key rates for an encoded quantum repeater

Sylvia Bratzik, Hermann Kampermann, Dagmar Bruß

We investigate secret key rates for the quantum repeater using encoding [L. Jiang et al., Phys. Rev. A 79, 032325 (2009)] and compare them to the standard repeater scheme by Briegel, D\"ur, Cirac, and Zoller. The former scheme has the advantage of a minimal consumption of classical communication. We analyze the trade-off in the secret key rate between the communication time and the required resources. For this purpose we introduce an error model for the repeater using encoding which allows for input Bell states with a fidelity smaller than one, in contrast to the model given by L. Jiang et al. [Phys. Rev. A 79, 032325 (2009)]. We show that one can correct additional errors in the encoded connection procedure of this repeater and develop a suitable decoding algorithm. Furthermore, we derive the rate of producing entangled pairs for the quantum repeater using encoding and give the minimal parameter values (gate quality and initial fidelity) for establishing a nonzero secret key. We find that the generic quantum repeater is optimal regarding the secret key rate per memory per second and show that the encoded quantum repeater using the simple three-qubit repetition code can even have an advantage with respect to the resources compared to other recent quantum repeater schemes with encoding.

arXiv:1401.6859•Physical Review A•Mar 31, 2014•26 citations

Memory imperfections in atomic-ensemble-based quantum repeaters

Jonatan Bohr Brask, Anders Søndberg Sørensen

Quantum repeaters promise to deliver long-distance entanglement overcoming loss in realistic quantum channels. A promising class of repeaters, based on atomic ensemble quantum memories and linear optics, follows the proposal by L.-M. Duan et al., Nature (London) 414, 413 (2001). Here we analyze this protocol in terms of a very general model for the quantum memories employed. We derive analytical expressions for scaling of entanglement with memory imperfections, dark counts, loss, and distance, and we apply our results to two specific quantum memory protocols. Our methods apply to any quantum memory with an interaction Hamiltonian at most quadratic in the mode operators and are in principle extendible to more recent modifications of the original proposal of Duan, Lukin, Cirac, and Zoller.

arXiv:0803.2069•Physical Review A•Jul 25, 2008•21 citations

Long-distance quantum key distribution with imperfect devices

Nicoló Lo Piparo, Mohsen Razavi

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.

arXiv:1210.8042•Physical Review A•Jul 30, 2013•23 citations

Device-independent secret-key-rate analysis for quantum repeaters

Timo Holz, Hermann Kampermann, Dagmar Bruß

The device-independent approach to quantum key distribution (QKD) aims to establish a secret key between two or more parties with untrusted devices, potentially under full control of a quantum adversary. The performance of a QKD protocol can be quantified by the secret key rate, which can be lower bounded via the violation of an appropriate Bell inequality in a setup with untrusted devices. We study secret key rates in the device-independent scenario for different quantum repeater setups and compare them to their device-dependent analogon. The quantum repeater setups under consideration are the original protocol by Briegel et al. [Phys. Rev. Lett. 81, 5932 (1998)] and the hybrid quantum repeater protocol by van Loock et al. [Phys. Rev. Lett. 96, 240501 (2006)]. For a given repeater scheme and a given QKD protocol, the secret key rate depends on a variety of parameters, such as the gate quality or the detector efficiency. We systematically analyze the impact of these parameters and suggest optimized strategies.

arXiv:1711.06072•Physical Review A•Jan 31, 2018•3 citations

Quantum key distribution over probabilistic quantum repeaters

Jeyran Amirloo, Mohsen Razavi, A. Hamed Majedi

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.

arXiv:1005.2503•Physical Review A•Sep 9, 2010•26 citations

Quantum repeaters and quantum key distribution: The impact of entanglement distillation on the secret key rate

Sylvia Bratzik, Silvestre Abruzzo, Hermann Kampermann +1 more

We investigate quantum repeaters in the context of quantum key distribution. We optimize the secret key rate per memory per second with respect to different distillation protocols and distillation strategies. For this purpose, we also derive an analytical expression for the average number of entangled pairs created by the quantum repeater, including classical communication times for entanglement swapping and entanglement distillation. We investigate the impact of this classical communication time on the secret key rate. Finally, we study the effect of the detector efficiency on the secret key rate.

arXiv:1303.3456•Physical Review A•Jun 26, 2013•52 citations
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 investigate secret key rates for the quantum repeater using encoding [L. Jiang et al., Phys. Rev. A 79, 032325 (2009)] and compare them to the standard repeater scheme by Briegel, D\"ur, Cirac, and Zoller. The former scheme has the advantage of a minimal consumption of classical communication. We analyze the trade-off in the secret key rate between the communication time and the required resources. For this purpose we introduce an error model for the repeater using encoding which allows for input Bell states with a fidelity smaller than one, in contrast to the model given by L. Jiang et al. [Phys. Rev. A 79, 032325 (2009)]. We show that one can correct additional errors in the encoded connection procedure of this repeater and develop a suitable decoding algorithm. Furthermore, we derive the rate of producing entangled pairs for the quantum repeater using encoding and give the minimal parameter values (gate quality and initial fidelity) for establishing a nonzero secret key. We find that the generic quantum repeater is optimal regarding the secret key rate per memory per second and show that the encoded quantum repeater using the simple three-qubit repetition code can even have an advantage with respect to the resources compared to other recent quantum repeater schemes with encoding.
Quantum repeaters promise to deliver long-distance entanglement overcoming loss in realistic quantum channels. A promising class of repeaters, based on atomic ensemble quantum memories and linear optics, follows the proposal by L.-M. Duan et al., Nature (London) 414, 413 (2001). Here we analyze this protocol in terms of a very general model for the quantum memories employed. We derive analytical expressions for scaling of entanglement with memory imperfections, dark counts, loss, and distance, and we apply our results to two specific quantum memory protocols. Our methods apply to any quantum memory with an interaction Hamiltonian at most quadratic in the mode operators and are in principle extendible to more recent modifications of the original proposal of Duan, Lukin, Cirac, and Zoller.
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 device-independent approach to quantum key distribution (QKD) aims to establish a secret key between two or more parties with untrusted devices, potentially under full control of a quantum adversary. The performance of a QKD protocol can be quantified by the secret key rate, which can be lower bounded via the violation of an appropriate Bell inequality in a setup with untrusted devices. We study secret key rates in the device-independent scenario for different quantum repeater setups and compare them to their device-dependent analogon. The quantum repeater setups under consideration are the original protocol by Briegel et al. [Phys. Rev. Lett. 81, 5932 (1998)] and the hybrid quantum repeater protocol by van Loock et al. [Phys. Rev. Lett. 96, 240501 (2006)]. For a given repeater scheme and a given QKD protocol, the secret key rate depends on a variety of parameters, such as the gate quality or the detector efficiency. We systematically analyze the impact of these parameters and suggest optimized strategies.
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.
We investigate quantum repeaters in the context of quantum key distribution. We optimize the secret key rate per memory per second with respect to different distillation protocols and distillation strategies. For this purpose, we also derive an analytical expression for the average number of entangled pairs created by the quantum repeater, including classical communication times for entanglement swapping and entanglement distillation. We investigate the impact of this classical communication time on the secret key rate. Finally, we study the effect of the detector efficiency on the secret key rate.