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Physical Review A

Comment on “Device-independent entanglement-based Bennett 1992 protocol”

Yong-Gang Tan, Qing-yu Cai

Published Jun 27, 2016• 2 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.93.066303

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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.
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 there were many proposals on device-independent (DI) quantum key distribution protocol whose security is based on the violation of the Clauser-Horne-Shimony-Holt inequality. However, as a statistical law, a certain extent of fluctuation has to be allowed. We show that the eavesdropper can make use of this property to obtain a remarkable part of the secret key by replacing some of the DI nonlocal boxes with local ones. On the contrary, the same cheating strategy does not apply to the device-dependent (DD) version of the protocol. Thus such kind of DI protocol is less secure than its DD counterpart.
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.
Device-independent quantum key distribution allows two users to set up shared cryptographic key without the need to trust the quantum devices used. Doing so requires nonlocal correlations between the users. However, in Farkas et al. [Phys. Rev. Lett. 127, 050503 (2021)PRLTAO0031-900710.1103/PhysRevLett.127.050503] it was shown that for known protocols nonlocality is not always sufficient, leading to the question of whether there is a fundamental lower bound on the minimum amount of nonlocality needed for any device-independent quantum key distribution implementation. Here, we show that no such bound exists, giving schemes that achieve key with correlations arbitrarily close to the local set. Furthermore, some of our constructions achieve the maximum of 1 bit of key per pair of entangled qubits. We achieve this by studying a family of Bell inequalities that constitute all self-tests of the maximally entangled state with a single linear Bell expression. Within this family there exist nonlocal correlations with the property that one pair of inputs yield outputs arbitrarily close to perfect key. Such correlations exist for a range of Clauser-Horne-Shimony-Holt values, including those arbitrarily close to the classical bound. Finally, we show the existence of quantum correlations that can generate both perfect key and perfect randomness simultaneously, while also displaying arbitrarily small Clauser-Horne-Shimony-Holt violation. This opens up the possibility of a new class of cryptographic protocol.
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.