Abstract
In this work, we present a new class of genuine multipartite Bell inequalities, that is particularly designed for multipartite device-independent (DI) quantum key distribution (QKD), also called DI conference key agreement. We prove the classical bounds of this inequality, discuss how to maximally violate it and show its usefulness by calculating achievable conference key rates via the violation of this Bell inequality. To this end, semidefinite programming techniques based on [Nat. Commun. 2, 238 (2011)] are employed and extended to the multipartite scenario. Our Bell inequality represents a nontrivial multipartite generalization of the Clauser-Horne-Shimony-Holt inequality and is motivated by the extension of the bipartite Bell state to the n-partite Greenberger-Horne-Zeilinger state. For DIQKD, we suggest an honest implementation for any number of parties and study the effect of noise on achievable asymptotic conference key rates.
Highlights
Among a variety of quantum technology applications [1,2,3], quantum key distribution (QKD) is one of the most prominent concepts, in particular for multiple parties in a quantum network [4]
In Ref. [18], a protocol to generate a secret key among n parties, called DI conference key agreement (DICKA) was introduced, which relies on the violation of the parity-CHSH inequality
We introduced a family of genuine multipartite Bell inequalities that is tailored to the n-GHZ state, while maintaining the possibility to maximally violate it with σz measurements
Summary
Among a variety of quantum technology applications [1,2,3], quantum key distribution (QKD) is one of the most prominent concepts, in particular for multiple parties in a quantum network [4]. At least one party has to use one measurement for key generation and for the Bell test, to detect a potential tampering of the devices. Achieving these requirements simultaneously should be guaranteed by the very structure of the Bell inequality. [4], perfectly correlated measurement results with the n-GHZ state can only be obtained if and only if all parties measure in the σz eigenbasis, which excludes maximum violation of the Bell inequalities in Refs. We propose an honest implementation for a multipartite DIQKD protocol and briefly discuss how noise affects the achievable asymptotic DI secret conference key rates
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