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

New Journal of Physics

Upper bound on device-independent quantum key distribution with two way classical postprocessing under individual attack

Yuzhe Zhang, Yi-Zheng Zhen, Feihu Xu

Published Nov 1, 2022• 3 citations
Publisher

Abstract

Abstract Device-independent quantum key distribution (DI-QKD) can guarantee the security even with untrusted devices. Unfortunately, conventional DI-QKD protocols can tolerate low noises only and require high detection efficiencies to achieve positive key rates. To improve the noise robustness, one promising solution is implementing the two-way classical postprocessing, which has the advantage of reducing the bit errors. In this paper, we study the DI-QKD with B-step two-way classical postprocessing under individual attacks. We adopt the tool of convex combination attack, i.e. an optimal individual attack, to upper bound the Devetak-Winter key rate. We show that, by using the B-step procedure, our protocol can tolerate detection efficiencies as low as 81.0 % and depolarising noise of 0.799, which is better than the thresholds for the protocol with one-way error correction. This result can serve as the lower bounds on the critical noise and detection efficiency for the scenarios under general attacks. Our work justifies the advantage of two-way classical postprocessing for DI-QKD, thus offering a step towards its applications.

DOI
10.1088/1367-2630/aca34b

Related papers

Upper bounds on key rates in device-independent quantum key distribution based on convex-combination attacks

Karol Łukanowski, Maria Balanzó-Juandó, Máté Farkas +2 more

The device-independent framework constitutes the most pragmatic approach to quantum protocols that does not put any trust in their implementations. It requires all claims, about e.g. security, to be made at the level of the final classical data in hands of the end-users. This imposes a great challenge for determining attainable key rates in device-independent quantum key distribution (DIQKD), but also opens the door for consideration of eavesdropping attacks that stem from the possibility of a given data being just generated by a malicious third-party. In this work, we explore this path and present the convex-combination attack as an efficient, easy-to-use technique for upper-bounding DIQKD key rates. It allows verifying the accuracy of lower bounds on key rates for state-of-the-art protocols, whether involving one-way or two-way communication. In particular, we demonstrate with its help that the currently predicted constraints on the robustness of DIQKD protocols to experimental imperfections, such as the finite visibility or detection efficiency, are already very close to the ultimate tolerable thresholds.

arXiv:2206.06245•Quantum•Dec 6, 2023•9 citations

Upper bounds for the secure key rate of the decoy-state quantum key distribution

Marcos Curty, Tobias Moroder, Xiongfeng Ma +2 more

The use of decoy states in quantum key distribution (QKD) has provided a method for substantially increasing the secret key rate and distance that can be covered by QKD protocols with practical signals. The security analysis of these schemes, however, leaves open the possibility that the development of better proof techniques or better classical postprocessing methods might further improve their performance in realistic scenarios. In this paper, we derive upper bounds on the secure key rate for decoy-state QKD. These bounds are based basically only on the classical correlations established by the legitimate users during the quantum communication phase of the protocol. The only assumption about the possible postprocessing methods is that double click events are randomly assigned to single click events. Further, we consider only secure key rates based on the uncalibrated device scenario which assigns imperfections such as detection inefficiency to the eavesdropper. Our analysis relies on two preconditions for secure two-way and one-way QKD. The legitimate users need to prove that there exists no separable state (in the case of two-way QKD) or that there exists no quantum state having a symmetric extension (one-way QKD) that is compatible with the available measurements results. Both criteria have been previously applied to evaluate single-photon implementations of QKD. Here we use them to investigate a realistic source of weak coherent pulses. The resulting upper bounds can be formulated as a convex optimization problem known as a semidefinite program which can be efficiently solved. For the standard four-state QKD protocol, they are quite close to known lower bounds, thus showing that there are clear limits to the further improvement of classical postprocessing techniques in decoy-state QKD.

arXiv:0901.4669•Physical Review A•Mar 26, 2009•10 citations

One-sided DI-QKD secure against coherent attacks over long distances

Michele Masini, Shubhayan Sarkar

Abstract Quantum key distribution (QKD) is a technique enabling provable secure communication but faces challenges in device characterisation, posing potential security risks. Device-independent (DI) QKD protocols overcome this issue by making minimal device assumptions but are limited in distance because they require high detection efficiencies, which refer to the ability of the experimental setup to detect quantum states. It is thus desirable to find QKD protocols that are based on realistic assumptions on the devices as well as implementable over long distances. In this work, we consider a one-sided DI QKD scheme with two measurements per party and show that it is secure against coherent attacks up to detection efficiencies greater than 50.1% specifically on the untrusted side. This is almost the theoretical limit achievable for protocols with two untrusted measurements. Interestingly, we also show that, by placing the source of states close to the untrusted side, our protocol is secure over distances comparable to standard QKD protocols.

arXiv:2403.11850•New Journal of Physics•May 14, 2026•4 citations

Device-Independent Quantum Key Distribution with Random Postselection

Feihu Xu, Yuzhe Zhang, Qiang Zhang +1 more

Device-independent quantum key distribution (QKD) can permit the superior security even with unknown devices. In practice, however, the realization of device-independent QKD is technically challenging because of its low noise tolerance. In the photonic setup, due to the limited detection efficiency, a large amount of the data generates from no-detection events which contain few correlations but contribute high errors. Here, we propose the device-independent QKD protocol with random postselection, where the secret keys are extracted only from the postselected subset of outcomes. This could not open the detection loophole as long as the entropy of the postselected subset is evaluated from the information of the entire set of data, including both detection and no-detection events. This postselection has the advantage to significantly reduce the error events, thus relaxing the threshold of required detection efficiency. In the model of collective attacks, our protocol can tolerate detector efficiency as low as 68.5%, which goes beyond standard security proofs. The results make a concrete step for the implementation of device-independent QKD in practice.

arXiv:2110.02701•Physical Review Letters•Mar 18, 2022•60 citations

Noise Resilience of Quantum Key Distribution Protocols Secured Against Independent Attacks With One-Way Communication

Adam Bílek, Ryszard Kukulski, Paulina Lewandowska +2 more

We investigate the resilience to noise of single-qubit quantum key distribution (QKD) protocols in the scenario of security against independent eavesdropping attacks and key distillation based on one-way classical communication. To this end, we introduce a noise-based metric that quantifies the efficiency of QKD protocols. Within this framework, we analyze the maximal noise levels that allow Alice and Bob to asymptotically establish a secure secret key. Using this assumption, we compare the noise tolerance of general single-qubit QKD protocols, in particular the BB84, B92, E91, and six-state protocols. Our main result determines the noise level threshold for QKD allowing one to distill an asymptotically secure secret key. Additionally, we demonstrate that the six-state protocol achieves the greatest resistance to noise while simultaneously yielding a higher post-selection efficiency than the other analyzed single-qubit protocols, confirming its robustness within the considered security model. Finally, we perform an analysis of the proposed noise-based metric and the conventional quantum bit error rate (QBER) metric.

quant-pharXiv:2607.11857•Jul 14, 2026•0 citations

Device-independent quantum key distribution based on Bell inequalities with more than two inputs and two outputs

Junior R. Gonzales-Ureta, Ana Predojević, Adán Cabello

Device-independent quantum key distribution (DI-QKD) offers the strongest form of security against eavesdroppers bounded by the laws of quantum mechanics. However, a practical implementation is still pending due to the requirement of combinations of visibility and detection efficiency that are beyond those possible with current technology. This mismatch motivates the search for DI-QKD protocols that can close the gap between theoretical and practical security. In this work, we present two DI-QKD protocols whose security relies on Bell inequalities with more than two inputs and two outputs. We show that, for maximally entangled states and perfect visibility, a protocol based on a Bell inequality with three inputs and four outputs requires a slightly lower detection efficiency than the protocols based on Bell inequalities with two inputs and two outputs.

arXiv:2104.00413•Physical Review A•May 28, 2021•25 citations
Abstract Device-independent quantum key distribution (DI-QKD) can guarantee the security even with untrusted devices. Unfortunately, conventional DI-QKD protocols can tolerate low noises only and require high detection efficiencies to achieve positive key rates. To improve the noise robustness, one promising solution is implementing the two-way classical postprocessing, which has the advantage of reducing the bit errors. In this paper, we study the DI-QKD with B-step two-way classical postprocessing under individual attacks. We adopt the tool of convex combination attack, i.e. an optimal individual attack, to upper bound the Devetak-Winter key rate. We show that, by using the B-step procedure, our protocol can tolerate detection efficiencies as low as 81.0 % and depolarising noise of 0.799, which is better than the thresholds for the protocol with one-way error correction. This result can serve as the lower bounds on the critical noise and detection efficiency for the scenarios under general attacks. Our work justifies the advantage of two-way classical postprocessing for DI-QKD, thus offering a step towards its applications.
The device-independent framework constitutes the most pragmatic approach to quantum protocols that does not put any trust in their implementations. It requires all claims, about e.g. security, to be made at the level of the final classical data in hands of the end-users. This imposes a great challenge for determining attainable key rates in device-independent quantum key distribution (DIQKD), but also opens the door for consideration of eavesdropping attacks that stem from the possibility of a given data being just generated by a malicious third-party. In this work, we explore this path and present the convex-combination attack as an efficient, easy-to-use technique for upper-bounding DIQKD key rates. It allows verifying the accuracy of lower bounds on key rates for state-of-the-art protocols, whether involving one-way or two-way communication. In particular, we demonstrate with its help that the currently predicted constraints on the robustness of DIQKD protocols to experimental imperfections, such as the finite visibility or detection efficiency, are already very close to the ultimate tolerable thresholds.
The use of decoy states in quantum key distribution (QKD) has provided a method for substantially increasing the secret key rate and distance that can be covered by QKD protocols with practical signals. The security analysis of these schemes, however, leaves open the possibility that the development of better proof techniques or better classical postprocessing methods might further improve their performance in realistic scenarios. In this paper, we derive upper bounds on the secure key rate for decoy-state QKD. These bounds are based basically only on the classical correlations established by the legitimate users during the quantum communication phase of the protocol. The only assumption about the possible postprocessing methods is that double click events are randomly assigned to single click events. Further, we consider only secure key rates based on the uncalibrated device scenario which assigns imperfections such as detection inefficiency to the eavesdropper. Our analysis relies on two preconditions for secure two-way and one-way QKD. The legitimate users need to prove that there exists no separable state (in the case of two-way QKD) or that there exists no quantum state having a symmetric extension (one-way QKD) that is compatible with the available measurements results. Both criteria have been previously applied to evaluate single-photon implementations of QKD. Here we use them to investigate a realistic source of weak coherent pulses. The resulting upper bounds can be formulated as a convex optimization problem known as a semidefinite program which can be efficiently solved. For the standard four-state QKD protocol, they are quite close to known lower bounds, thus showing that there are clear limits to the further improvement of classical postprocessing techniques in decoy-state QKD.
Abstract Quantum key distribution (QKD) is a technique enabling provable secure communication but faces challenges in device characterisation, posing potential security risks. Device-independent (DI) QKD protocols overcome this issue by making minimal device assumptions but are limited in distance because they require high detection efficiencies, which refer to the ability of the experimental setup to detect quantum states. It is thus desirable to find QKD protocols that are based on realistic assumptions on the devices as well as implementable over long distances. In this work, we consider a one-sided DI QKD scheme with two measurements per party and show that it is secure against coherent attacks up to detection efficiencies greater than 50.1% specifically on the untrusted side. This is almost the theoretical limit achievable for protocols with two untrusted measurements. Interestingly, we also show that, by placing the source of states close to the untrusted side, our protocol is secure over distances comparable to standard QKD protocols.
Device-independent quantum key distribution (QKD) can permit the superior security even with unknown devices. In practice, however, the realization of device-independent QKD is technically challenging because of its low noise tolerance. In the photonic setup, due to the limited detection efficiency, a large amount of the data generates from no-detection events which contain few correlations but contribute high errors. Here, we propose the device-independent QKD protocol with random postselection, where the secret keys are extracted only from the postselected subset of outcomes. This could not open the detection loophole as long as the entropy of the postselected subset is evaluated from the information of the entire set of data, including both detection and no-detection events. This postselection has the advantage to significantly reduce the error events, thus relaxing the threshold of required detection efficiency. In the model of collective attacks, our protocol can tolerate detector efficiency as low as 68.5%, which goes beyond standard security proofs. The results make a concrete step for the implementation of device-independent QKD in practice.
We investigate the resilience to noise of single-qubit quantum key distribution (QKD) protocols in the scenario of security against independent eavesdropping attacks and key distillation based on one-way classical communication. To this end, we introduce a noise-based metric that quantifies the efficiency of QKD protocols. Within this framework, we analyze the maximal noise levels that allow Alice and Bob to asymptotically establish a secure secret key. Using this assumption, we compare the noise tolerance of general single-qubit QKD protocols, in particular the BB84, B92, E91, and six-state protocols. Our main result determines the noise level threshold for QKD allowing one to distill an asymptotically secure secret key. Additionally, we demonstrate that the six-state protocol achieves the greatest resistance to noise while simultaneously yielding a higher post-selection efficiency than the other analyzed single-qubit protocols, confirming its robustness within the considered security model. Finally, we perform an analysis of the proposed noise-based metric and the conventional quantum bit error rate (QBER) metric.
Device-independent quantum key distribution (DI-QKD) offers the strongest form of security against eavesdroppers bounded by the laws of quantum mechanics. However, a practical implementation is still pending due to the requirement of combinations of visibility and detection efficiency that are beyond those possible with current technology. This mismatch motivates the search for DI-QKD protocols that can close the gap between theoretical and practical security. In this work, we present two DI-QKD protocols whose security relies on Bell inequalities with more than two inputs and two outputs. We show that, for maximally entangled states and perfect visibility, a protocol based on a Bell inequality with three inputs and four outputs requires a slightly lower detection efficiency than the protocols based on Bell inequalities with two inputs and two outputs.