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Journal of Modern Optics

Bell's Inequality and Rejected-data Protocols for Quantum Cryptography

Stephen Mark Barnett, Simon J. D. Phoenix

Published Aug 1, 1993• 16 citations
Publisher

Abstract

We introduce a suitably constructed Bell inequality as a test of the integrity of a single-particle quantum cryptography scheme.
DOI
10.1080/09500349314551511

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Physical Review A•Nov 15, 2023•0 citations
We show that rejected-data protocols for quantum cryptography are secure against generalized intercept/resend strategies of an eavesdropper provided that the legitimate users of the communication channel use at least three bases. We discuss the connection between this result and the recently-developed protocol based on violations of a suitably-constructed Bell-type inequality for single particles. We also give a new estimate of the probability that an eavesdropper remains undetected under the original protocol and thereby show that the optimal strategies available to an eavesdropper are further limited to those which randomize the errors between the sub-ensembles of data. This result also has implications for the way in which the legitimate users of the channel choose their test data.
Closing the fair sampling loophole in Bell-type experiments is crucial for a better understanding of the fundamentals of quantum mechanics and for realizing the security of quantum cryptography. However, an experimental demonstration of a Bell test without the fair sampling loophole is challenging. A central obstacle in photonic implementations is that the sampling efficiency, including the collection and detection efficiencies, must be above a certain threshold. We here investigate the minimum sampling efficiency for violating a multiparticle Bell inequality in an asymmetric configuration. The results show that the minimum sampling efficiency is arbitrarily close to 1n\frac{1}{n}n1​ in the nnn-particle system. Since the security of device-independent quantum key distribution (DI-QKD) protocols relies on the violation of a Bell inequality, we also investigate the application of the asymmetric Bell test in quantum cryptography. Based on the standard DI-QKD protocol, we demonstrate that the minimum sampling efficiency for extracting secure keys is reduced from 92.492.4%92.4 to 84.484.4%84.4. Therefore, we believe our work can serve as a recipe for experimentalists planning to implement DI-QKD.