Realizing secure communication between distant parties is one of the main goals of quantum technology. Although quantum key distribution (QKD) promises information-theoretic security for sharing a secret key, the key rate heavily depends on the level of noise in the quantum channel. To overcome the noise, both quantum and classical techniques exist, i.e., entanglement distillation and classical advantage distillation. So far, these techniques have only been used separately from each other. Herein, we present a two-stage distillation scheme concatenating entanglement distillation with classical advantage distillation. For the advantage distillation, we utilize a fixed protocol, specifically, the repetition code; in the case of entanglement distillation, we employ an enumeration algorithm to find an optimal protocol. We test our scheme for noisy entangled states and demonstrate its quantitative advantage: Our two-stage distillation scheme achieves finite key rates even in a high-noise regime where entanglement distillation or advantage distillation alone cannot afford key sharing. We also calculate the security bounds for relevant QKD protocols with our key-distillation scheme and show that they exceed the previous security bounds on the critical quantum bit error rates with only advantage distillation. Since the advantage distillation part does not introduce further requirements for quantum resources other than those required for entanglement distillation, the proposed scheme is well suited for quantum key distribution tasks with entanglement distribution networks.
Realizing secure communication between distant parties is one of the main goals of quantum technology. Although quantum key distribution (QKD) promises information-theoretic security for sharing a secret key, the key rate heavily depends on the level of noise in the quantum channel. To overcome the noise, both quantum and classical techniques exist, i.e., entanglement distillation and classical advantage distillation. So far, these techniques have only been used separately from each other. Herein, we present a two-stage distillation scheme concatenating entanglement distillation with classical advantage distillation. For the advantage distillation, we utilize a fixed protocol, specifically, the repetition code; in the case of entanglement distillation, we employ an enumeration algorithm to find an optimal protocol. We test our scheme for noisy entangled states and demonstrate its quantitative advantage: Our two-stage distillation scheme achieves finite key rates even in a high-noise regime where entanglement distillation or advantage distillation alone cannot afford key sharing. We also calculate the security bounds for relevant QKD protocols with our key-distillation scheme and show that they exceed the previous security bounds on the critical quantum bit error rates with only advantage distillation. Since the advantage distillation part does not introduce further requirements for quantum resources other than those required for entanglement distillation, the proposed scheme is well suited for quantum key distribution tasks with entanglement distribution networks.
Quantum Key Distribution (QKD) allows two legitimate parties, Alice and Bob, to share a secret key with information-theoretic security, ensuring that an eavesdropper, Eve, cannot obtain any information about the key. A QKD protocol is provably secure only when the Quantum Bit Error Rate (QBER) is below a certain threshold and, therefore, the presence of noise inherently limits the maximum transmission distance. Advantage Distillation (AD) is a classical post-processing technique that enhances QKD protocols by increasing the maximum acceptable QBER and, thus, allows extending the communication range. AD operates by post-selecting blocks of bits and extracting fewer but highly correlated bits between Alice and Bob, which exhibit a reduced QBER, thus lowering the amount of information that has to be disclosed during the information reconciliation step. In this study, we present a new analytical expression for the secure key rate. This will enable a finite-size secure key length analysis of the decoy state version of the BB84 protocol including AD post-processing.
Device-independent quantum secret sharing (DI-QSS) provides high security by eliminating the need to trust devices, yet its practical performance is limited by channel loss and noise. This work extends advantage distillation from two-party quantum key distribution (QKD) to three-party DI-QSS, redesigning the corresponding data interaction and verification procedures. The technique is systematically applied to the basic protocol and three active improvement strategies: noise preprocessing, post-selection, and their combination. This approach enhances noise tolerance, reduces the required global detection efficiency threshold, and significantly extends the maximum secure communication distance. Numerical simulations demonstrate that for the basic protocol over fiber, the maximum secure distance increases from 0.16 km to 1.85 km, and the noise tolerance improves from 10.17% to 28.49%. The results show that generalizing advantage distillation to the three-party setting effectively strengthens the protocol's robustness and practicality, enhancing its adaptability to realistic noise and advancing the development of more reliable quantum secret sharing systems.
Abstract Quantum key distribution promises information-theoretically secure communication, with data post-processing playing a vital role in extracting secure keys from raw data. While hardware advancements have significantly improved practical implementations, optimizing post-processing techniques offers a cost-effective avenue to enhance performance. Advantage distillation, which extends beyond standard information reconciliation and privacy amplification, has proven instrumental in various post-processing methods. However, the optimal post-processing remains an open question. Therefore, it is important to develop a comprehensive framework to encapsulate and enhance these existing methods. In this work, we propose an advantage distillation framework for quantum key distribution, generalizing and unifying existing key distillation protocols. Inspired by entanglement distillation, our framework not only integrates current techniques but also improves upon them. Notably, by employing classical linear codes, we achieve higher key rates, particularly in scenarios where one-time pad encryption is not used for post-processing. Our approach provides insights into existing protocols and offers a systematic way for further enhancements in quantum key distribution.
Device-independent quantum key distribution (DIQKD) aims to mitigate adversarial exploitation of imperfections in quantum devices by providing an approach for secret key distillation with modest security assumptions. Advantage distillation, a two-way communication procedure in error correction, has proven effective in raising noise tolerances in both device-dependent and device-independent QKD. Previously, device-independent security proofs against independent and identically distributed (IID) collective attacks were developed for an advantage distillation protocol known as the repetition-code protocol, based on security conditions involving the fidelity between some states in the protocol. However, there exists a gap between the sufficient and necessary security conditions, which hinders the calculation of tight noise-tolerance bounds based on the fidelity. We close this gap by presenting an alternative proof structure that replaces the fidelity with the quantum Chernoff divergence, a distinguishability measure that arises in symmetric hypothesis testing. Working in the IID collective attacks model, we derive matching sufficient and necessary conditions for the repetition-code protocol to be secure (up to a natural conjecture regarding the latter case) in terms of the quantum Chernoff divergence, hence indicating that this serves as the relevant quantity of interest for this protocol. Furthermore, using this security condition we obtain some improvements over previous results on the noise tolerance thresholds for DIQKD. Our results provide insight into a fundamental question in quantum information theory regarding the circumstances under which DIQKD is possible.
Quantum key distribution (QKD) is a promising method for sharing an information-theoretically secure secret key using the properties of quantum mechanics. Although QKD is the most practical field in quantum information science, its widespread adoption is constrained by high implementation costs. Despite the cost-effectiveness of propagating QKD with classical communication using wavelength division multiplexing (WDM), the noise generated by relatively strong classical signals degrades QKD performance. Even though several mitigation strategies exist, they often involve complexity or additional hardware. In this paper, we apply advantage distillation (AD) to enhance the performance of a practical decoy-state BB84 QKD system operating in a WDM environment. We perform finite-key analysis in both co-propagation and counter-propagation scenarios with three classical channels, and furthermore we examine the effects of varying the number of classical channels and the optical power per channel. A comparison of simulation results obtained with and without AD demonstrates that AD is robust to noise originating from classical channels. These results show that AD increases the secure key rate and transmission distance in the WDM-based QKD environment under both co-propagation and counter-propagation without requiring hardware changes. These findings suggest advantage distillation is a promising strategy for the widespread adoption of WDM-based QKD, including in challenging counter-propagation cases.
Quantum key distribution (QKD) achieves information-theoretic security for a shared secret key, using distributed quantum states. To establish secret bits, two honest parties apply key distillation protocols to the resulting measurement outcomes. In this work, we establish a rigorous connection between the key rate achievable by applying two-way key distillation, such as advantage distillation, and quantum hypothesis testing, via an integral representation of the conditional entropy in terms of the error probabilities of binary state discrimination. This connection significantly improves bounds on key rates at finite blocklengths relative to existing fidelity-based bounds. Moreover, in an important special case, it closes the gap between the known sufficient and conjectured necessary conditions for key generation in the large-blocklength limit. More generally, it establishes a matching asymptotic necessary condition, leaving the corresponding finite-blocklength result open. More broadly, our work shows how results in quantum hypothesis testing can directly sharpen the security analysis of QKD.