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arXiv:1111.1997 · Physical Review A

Device-independent entanglement-based Bennett 1992 protocol

Marco Lucamarini, Giuseppe Vallone, Ilaria Gianani, Paolo Mataloni, Giovanni Di Giuseppe

Published Sep 18, 2012• 23 citations
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Abstract

In this paper we set forth a connection between the Bennett 1992 protocol and a Bell inequality. This allows us to extend the usual prepare-and-measure protocol to its entanglement-based formulation. We exploit a recent result in the framework of device-independent quantum key distribution to provide a simple, model-independent, security proof for the protocol. The minimum efficiency required for a practical implementation of the scheme can be as low as 75% in the completely untrusted case and 50% in case the sender is assumed to be trusted.

DOI
10.1103/physreva.86.032325

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Our paper [Phys. Rev. A 86, 032325 (2012)], setting forth a previously unknown connection between the Bennett 1992 protocol and a Bell inequality, has recently received a Comment [Phys. Rev. A 93, 066303 (2016)] about a possible flaw in its potential device-independent (DI) implementation. We point the authors of the Comment to prior works showing that what they assume to be specific to our protocol's DI implementation is actually a standard assumption in DI quantum key distribution. Therefore there is no need to revise any of the conclusions drawn in Lucamarini et al. [Phys. Rev. A 86, 032325 (2012)].

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Recently, Lucamarini et al. proposed the device-independent entanglement-based Bennett 1992 protocol [Phys. Rev. A 86, 032325 (2012)]. By exploiting the results in device-independent quantum key distribution with the Clauser-Horne-Shimony-Holt inequality, they claimed the security of their protocol. We will show, however, the way of encoding and the process for the latent eavesdropper to obtain the illegal information are different in these two protocols. Thus the security of their protocol cannot rely on Bell's theorem only.

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In this paper we set forth a connection between the Bennett 1992 protocol and a Bell inequality. This allows us to extend the usual prepare-and-measure protocol to its entanglement-based formulation. We exploit a recent result in the framework of device-independent quantum key distribution to provide a simple, model-independent, security proof for the protocol. The minimum efficiency required for a practical implementation of the scheme can be as low as 75% in the completely untrusted case and 50% in case the sender is assumed to be trusted.
Our paper [Phys. Rev. A 86, 032325 (2012)], setting forth a previously unknown connection between the Bennett 1992 protocol and a Bell inequality, has recently received a Comment [Phys. Rev. A 93, 066303 (2016)] about a possible flaw in its potential device-independent (DI) implementation. We point the authors of the Comment to prior works showing that what they assume to be specific to our protocol's DI implementation is actually a standard assumption in DI quantum key distribution. Therefore there is no need to revise any of the conclusions drawn in Lucamarini et al. [Phys. Rev. A 86, 032325 (2012)].
Recently, Lucamarini et al. proposed the device-independent entanglement-based Bennett 1992 protocol [Phys. Rev. A 86, 032325 (2012)]. By exploiting the results in device-independent quantum key distribution with the Clauser-Horne-Shimony-Holt inequality, they claimed the security of their protocol. We will show, however, the way of encoding and the process for the latent eavesdropper to obtain the illegal information are different in these two protocols. Thus the security of their protocol cannot rely on Bell's theorem only.
Device- independent quantum key distribution is the art of establishing secure keys over untrusted channels even when using potentially untrusted devices [1]. It allows the users to check the secure functioning of the underlying quantum devices by a statistical test using a Bell inequality, thereby also ensuring security against implementation flaws-a major vulnerability to quantum key distribution protocols realized so far. An experimental realisation, however, is challenging because it demands high-quality entanglement shared between two remote locations that can be detected with high efficiency.
Most of the existing quantum key distribution protocols do not consider the fact that the source and measuring device cannot be trusted, which causes hidden danger, such as the side channel attack, resulting in unsafe quantum communication. Therefore, it is important to research quantum key distribution protocol under the conditions of non-trusted device. We show a quantum key distribution protocol from correlation that violates a Bell inequality under the condition that both the source and the measurement devices are untrusted. We analyze its security under minimal assumptions (the non-signaling principle). We take noises and detection efficiency of the user's (Alice and Bob) detectors into account when bounding the secret key rate. We achieve a lower detection efficiency threshold, to compare with Ref. [Phys. Rev. A 85, 010301, (2012)], which means in the case of low efficiency of the detector, the key distribution can also be successfully completed.
Device-independent security is the gold standard for quantum cryptography: not only is security based entirely on the laws of quantum mechanics, but it holds irrespective of any a priori assumptions on the quantum devices used in a protocol, making it particularly applicable in a quantum-wary environment. While the existence of device-independent protocols for tasks such as randomness expansion and quantum key distribution has recently been established, the underlying proofs of security remain very challenging, yield rather poor key rates, and demand very high quality quantum devices, thus making them all but impossible to implement in practice. We introduce a technique for the analysis of device-independent cryptographic protocols. We provide a flexible protocol and give a security proof that provides quantitative bounds that are asymptotically tight, even in the presence of general quantum adversaries. At a high level our approach amounts to establishing a reduction to the scenario in which the untrusted device operates in an identical and independent way in each round of the protocol. This is achieved by leveraging the sequential nature of the protocol and makes use of a newly developed tool, the “entropy accumulation theorem” of Dupuis, Fawzi, and Renner [ Entropy Accumulation, preprint, 2016]. As concrete applications we give simple and modular security proofs for device-independent quantum key distribution and randomness expansion protocols based on the CHSH inequality. For both tasks, we establish essentially optimal asymptotic key rates and noise tolerance. In view of recent experimental progress, which has culminated in loophole-free Bell tests, it is likely that these protocols can be practically implemented in the near future.
Quantum cryptography promises levels of security that are impossible to replicate in a classical world. Can this security be guaranteed even when the quantum devices on which the protocol relies are untrusted? This central question dates back to the early 1990s when the challenge of achieving device-independent quantum key distribution was first formulated. We answer this challenge by rigorously proving the device-independent security of a slight variant of Ekert's original entanglement-based protocol against the most general (coherent) attacks. The resulting protocol is robust: While assuming only that the devices can be modeled by the laws of quantum mechanics and are spatially isolated from each other and from any adversary's laboratory, it achieves a linear key rate and tolerates a constant noise rate in the devices. In particular, the devices may have quantum memory and share arbitrary quantum correlations with the eavesdropper. The proof of security is based on a new quantitative understanding of the monogamous nature of quantum correlations in the context of a multiparty protocol.