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arXiv:2212.06975 · Physical Review A

Quantum Chernoff divergence in advantage distillation for quantum key distribution and device-independent quantum key distribution

Mikka Stasiuk, Norbert Lütkenhaus, Ernest Y.-Z. Tan

Published Feb 27, 2025• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.111.022631

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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.
Device-independent quantum key distribution (DIQKD) offers the prospect of distributing secret keys with only minimal security assumptions, by making use of a Bell violation. However, existing DIQKD security proofs have low noise tolerances, making a proof-of-principle demonstration currently infeasible. We investigate whether the noise tolerance can be improved by using advantage distillation, which refers to using two-way communication instead of the one-way error correction currently used in DIQKD security proofs. We derive an efficiently verifiable condition to certify that advantage distillation is secure against collective attacks in a variety of DIQKD scenarios, and use this to show that it can indeed allow higher noise tolerances, which could help to pave the way towards an experimental implementation of DIQKD.
Abstract It is known that advantage distillation (that is, information reconciliation using two-way communication) improves noise tolerances for quantum key distribution (QKD) setups. Two-way communication is hence also of interest in the device-independent case, where noise tolerance bounds for one-way error correction are currently too low to be experimentally feasible. Existing security proofs for the device-independent repetition-code protocol (the most prominent form of advantage distillation) rely on fidelity-related security conditions, but previous bounds on the fidelity were not tight. We improve on those results by developing an algorithm that returns arbitrarily tight lower bounds on the fidelity. Our results give insight on how strong the fidelity-related security conditions are, and could also be used to compute some lower bounds on one-way protocol keyrates. Finally, we conjecture a necessary security condition for the protocol studied in this work, that naturally complements the existing sufficient conditions.
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.
Low noise tolerances for current device-independent quantum key distribution protocols and the existence of fidelity-related security conditions in device-independent advantage distillation motivate the need for strong lower bounds on the fidelity.This thesis shows that a reduction to qubits does not deliver optimal bounds.An algorithm is derived that can in principle bound the fidelity for our device-independent setup to an arbitrary precision.This algorithm is computable with a semi-definite program and a constraint optimization.We conclude with a conjecture for a necessary security condition against collective attacks, where a repetition-code protocol that applies advantage distillation is considered.
Device-independent quantum key distribution (DIQKD) aims to achieve secure key distribution with only minimal assumptions, by basing its security on the violation of Bell inequalities. While this offers strong security guarantees, it comes at the cost of being challenging to implement experimentally. In this thesis, we present security proofs for several techniques that help to improve the keyrates and noise tolerance of DIQKD, such as noisy preprocessing, random key measurements, and advantage distillation. We also show finite-size security proofs for some protocols based on combining several of these techniques. These results and proof techniques should be useful for further development of DIQKD protocols.
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.