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arXiv:1903.10535 · Physical Review Letters

Advantage Distillation for Device-Independent Quantum Key Distribution

Ernest Y.-Z. Tan, Charles Ci Wen Lim, Renato Renner

Published Jan 16, 2020• 69 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.124.020502

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•Jan 1, 2021•1 citation
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.
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.
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.
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 key distribution (DIQKD) represents a relaxation of the security assumptions made in usual quantum key distribution (QKD). As in usual QKD, the security of DIQKD follows from the laws of quantum physics, but contrary to usual QKD, it does not rely on any assumptions about the internal working of the quantum devices used in the protocol. In this paper, we present in detail the security proof for a DIQKD protocol introduced in Acín et al (2008 Phys. Rev. Lett. 98 230501). This proof exploits the full structure of quantum theory (as opposed to other proofs that exploit only the no-signaling principle), but only holds against collective attacks, where the eavesdropper is assumed to act on the quantum systems of the honest parties independently and identically in each round of the protocol (although she can act coherently on her systems at any time). The security of any DIQKD protocol necessarily relies on the violation of a Bell inequality. We discuss the issue of loopholes in Bell experiments in this context.
Abstract Device-independent quantum key distribution (DIQKD) generates a secret key among two parties in a provably secure way without making assumptions about the internal working of the devices used in the protocol. The main challenge for a DIQKD physical implementation is that the data observed among the two parties must violate a Bell inequality without fair-sampling, since otherwise the observed correlations can be faked with classical resources and security can no longer be guaranteed. In spite of the advances recently made to achieve higher detection efficiencies in Bell experiments, DIQKD remains experimentally difficult at long distances due to the exponential increase of loss in the channel separating the two parties. Here we describe and analyze plausible solutions to overcome the crucial problem of channel loss in the frame of DIQKD physical implementations.
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.