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arXiv:1910.11360 · Physical Review Research

Genuine multipartite Bell inequality for device-independent conference key agreement

Timo Holz, Hermann Kampermann, Dagmar Bruß

Published May 29, 2020• 38 citations
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Abstract

The authors introduce a new family of multipartite Bell inequalities and analytically characterize their features. The paper demonstrates the usefulness of the relations for multipartite device-independent quantum key distribution, which requires inequalities with a specific structure.
DOI
10.1103/physrevresearch.2.023251

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The Bell inequality can provide a useful witness for device-independent applications with quantum (or postquantum) eavesdroppers. This feature holds only for single entangled systems. Our goal is to explore a device-independent model for quantum networks. We first propose a Bell inequality to verify the genuinely multipartite nonlocality of connected quantum networks including cyclic networks and universal quantum computational resources for a measurement-based computation model. This is further used to construct a monogamy relation in a fully device-independent model with multisource quantum resources. It is finally applied for multiparty quantum key distribution, blind quantum computation, and quantum secret sharing. The present model can inspire various large-scale applications on quantum networks in a device-independent manner.
Multipartite device-independent quantum key distribution (DI-QKD), also known as device-independent conference key agreement, enables more than two remote parties to share a common key with information-theoretic security even without trusting the devices. So far, several multipartite DI-QKD protocols have been proposed where Greenberger-Horne-Zeilinger (GHZ) states are used as multipartite entanglement. A natural question is then whether one can construct multipartite DI-QKD with the other type of multipartite entanglement. W state is of particular interest since it is intrinsically different from GHZ state and in some cases, easier to optically implement. In this paper, we show that multipartite DI-QKD is possible with W states. To this end, we construct Bell inequalities largely violated by W states, which can be used for the multipartite DI-QKD. Furthermore, we consider several different implementation scenarios. First, we analyze the minimum required detection efficiencies to extract finite amount of keys. Then we propose a long-distance multipartite DI-QKD protocol with single-photon interference and make detailed analyses with several physical implementation scenarios. We show that the protocol enables secret key distribution over longer distances than the existing multipartite DI-QKD protocols based on GHZ states. This study provides new insight about the relationship between multipartite entanglement and device-independent quantum information processing as well as opens an alternative path toward long-distance multipartite DI-QKD.
Conference key agreement allows multiple remote parties to establish a shared secret key with information-theoretical security. In device-independent conference key agreement, security can be guaranteed with minimal assumptions on the devices used, provided that a violation of a Bell inequality is observed. However, implementations are extremely challenging because high detection efficiency is required to observe loophole-free Bell violations. Here, we enhance the robustness of device-independent conference key agreement by introducing a new family of multipartite Bell inequalities called the asymmetric parity-Clauser-Horne-Shimony-Holt (CHSH) inequalities. We derive a tight analytical lower bound on the conditional von Neumann entropy of the outcomes of one of the parties in a protocol based on this inequality, including noisy preprocessing. Using this bound, we analyze robustness to detection inefficiencies as well as local and global depolarizing noise. We show that the combination of the asymmetric parity-CHSH inequality and noisy preprocessing can significantly improve the robustness to imperfections.
We present a security analysis of conference key agreement (CKA) in the most adversarial model of device independence (DI). Our protocol can be implemented by any experimental setup that is capable of performing Bell tests [specifically, the Mermin-Ardehali-Belinskii-Klyshko (MABK) inequality], and security can in principle be obtained for any violation of the MABK inequality that detects genuine multipartite entanglement among the NNN parties involved in the protocol. As our main tool, we derive a direct physical connection between the NNN-partite MABK inequality and the Clauser-Horne-Shimony-Holt (CHSH) inequality, showing that certain violations of the MABK inequality correspond to a violation of the CHSH inequality between one of the parties and the other $N\ensuremath{-}1$. We compare the asymptotic key rate for device-independent conference key agreement (DICKA) to the case where the parties use $N\ensuremath{-}1$ device-independent quantum key distribution protocols in order to generate a common key. We show that for some regime of noise the DICKA protocol leads to better rates.