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arXiv:2111.04482 · Physical Review A

Device-independent secret key rates via a postselected Bell inequality

Sarnava Datta, Hermann Kampermann, Dagmar Bruß

Published Mar 29, 2022• 2 citations
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Abstract

In device-independent quantum key distribution (DIQKD) the security is not based on any assumptions about the intrinsic properties of the devices and the quantum signals but on the violation of a Bell inequality. We introduce a DIQKD scenario in which an optimal Bell inequality is constructed from the performed measurement data rather than fixing beforehand a specific Bell inequality. Our method can be employed in a general way, for any number of measurement settings and any number of outcomes. We provide an implementable DIQKD protocol and perform finite-size security key analysis for collective attacks. We compare our approach with related procedures in the literature and analyze the robustness of our protocol. We also study the performance of our method in several Bell scenarios as well as for random measurement settings.

DOI
10.1103/physreva.105.032451

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In device-independent quantum key distribution (DIQKD) the security is not based on any assumptions about the intrinsic properties of the devices and the quantum signals but on the violation of a Bell inequality. We introduce a DIQKD scenario in which an optimal Bell inequality is constructed from the performed measurement data rather than fixing beforehand a specific Bell inequality. Our method can be employed in a general way, for any number of measurement settings and any number of outcomes. We provide an implementable DIQKD protocol and perform finite-size security key analysis for collective attacks. We compare our approach with related procedures in the literature and analyze the robustness of our protocol. We also study the performance of our method in several Bell scenarios as well as for random measurement settings.
Abstract Device-independent quantum key distribution (DIQKD) provides the strongest form of secure key exchange, using only the input–output statistics of the devices to achieve information-theoretic security. Although the basic security principles of DIQKD are now well understood, it remains a technical challenge to derive reliable and robust security bounds for advanced DIQKD protocols that go beyond the previous results based on violations of the CHSH inequality. In this work, we present a framework based on semidefinite programming that gives reliable lower bounds on the asymptotic secret key rate of any QKD protocol using untrusted devices. In particular, our method can in principle be utilized to find achievable secret key rates for any DIQKD protocol, based on the full input–output probability distribution or any choice of Bell inequality. Our method also extends to other DI cryptographic tasks.
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 In the implementation of device-independent (DI) quantum key distribution (QKD) we are interested in maximizing the key rate, i.e. the number of key bits that can be obtained per signal, for a fixed security parameter. In the finite size regime, we furthermore also care about the minimum number of signals required before key can be obtained at all. Here, we perform a fully finite size analysis of device independent protocols using the CHSH inequality both for collective and coherent attacks. For coherent attacks, we sharpen the results recently derived in Arnon-Friedman et al (2018 Nat. Commun. 9 459), to reduce the minimum number of signals before key can be obtained. In the regime of collective attacks, where the devices are restricted to have no memory, we employ two different techniques that exploit this restriction to further reduce the number of signals. We then discuss experimental platforms in which DIQKD may be implemented. We analyse Bell violations and expected QBER achieved in previous Bell tests with distant setups and situate these parameters in the security analysis. Moreover, focusing on one of the experimental platforms, namely nitrogen-vacancy based systems, we describe experimental improvements that can lead to a DI QKD implementation in the near future.
We provide an analysis of a family of device-independent quantum key distribution (QKD) protocols that has the following features. (a) The bits used for the secret key do not come from the results of the measurements on an entangled state but from the choices of settings. (b) Instead of a single security parameter (a violation of some Bell inequality) a set of them is used to estimate the level of trust in the secrecy of the key. The main advantage of these protocols is a smaller vulnerability to imperfect random number generators made possible by feature (a). We prove the security and the robustness of such protocols. We show that using our method it is possible to construct a QKD protocol which retains its security even if the source of randomness used by communicating parties is strongly biased. As a proof of principle, an explicit example of a protocol based on the Hardy's paradox is presented. Moreover, in the noiseless case, the protocol is secure in a natural way against any type of memory attack, and thus allows one to reuse the device in subsequent rounds. We also analyze the robustness of the protocol using semidefinite programming methods. Finally, we present a postprocessing method, and observe a paradoxical property that rejecting some random part of the private data can increase the key rate of the protocol.
Abstract Device-independent quantum key distribution (DIQKD) is the art of using untrusted devices to distribute secret keys in an insecure network. It thus represents the ultimate form of cryptography, offering not only information-theoretic security against channel attacks, but also against attacks exploiting implementation loopholes. In recent years, much progress has been made towards realising the first DIQKD experiments, but current proposals are just out of reach of today’s loophole-free Bell experiments. Here, we significantly narrow the gap between the theory and practice of DIQKD with a simple variant of the original protocol based on the celebrated Clauser-Horne-Shimony-Holt (CHSH) Bell inequality. By using two randomly chosen key generating bases instead of one, we show that our protocol significantly improves over the original DIQKD protocol, enabling positive keys in the high noise regime for the first time. We also compute the finite-key security of the protocol for general attacks, showing that approximately 108–1010 measurement rounds are needed to achieve positive rates using state-of-the-art experimental parameters. Our proposed DIQKD protocol thus represents a highly promising path towards the first realisation of DIQKD in practice.
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.