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arXiv:1012.3878

Device-Independent Quantum Key Distribution

Esther Hänggi

Published Jan 1, 2010• 23 citations
arXivHTMLPDF

Abstract

In this thesis, we study two approaches to achieve device-independent quantum key distribution: in the first approach, the adversary can distribute any system to the honest parties that cannot be used to communicate between the three of them, i.e., it must be non-signalling. In the second approach, we limit the adversary to strategies which can be implemented using quantum physics. For both approaches, we show how device-independent quantum key distribution can be achieved when imposing an additional condition. In the non-signalling case this additional requirement is that communication is impossible between all pairwise subsystems of the honest parties, while, in the quantum case, we demand that measurements on different subsystems must commute. We give a generic security proof for device-independent quantum key distribution in these cases and apply it to an existing quantum key distribution protocol, thus proving its security even in this setting. We also show that, without any additional such restriction there always exists a successful joint attack by a non-signalling adversary.

DOI
10.3929/ethz-a-006264278

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In this thesis, we study two approaches to achieve device-independent quantum key distribution: in the first approach, the adversary can distribute any system to the honest parties that cannot be used to communicate between the three of them, i.e., it must be non-signalling. In the second approach, we limit the adversary to strategies which can be implemented using quantum physics. For both approaches, we show how device-independent quantum key distribution can be achieved when imposing an additional condition. In the non-signalling case this additional requirement is that communication is impossible between all pairwise subsystems of the honest parties, while, in the quantum case, we demand that measurements on different subsystems must commute. We give a generic security proof for device-independent quantum key distribution in these cases and apply it to an existing quantum key distribution protocol, thus proving its security even in this setting. We also show that, without any additional such restriction there always exists a successful joint attack by a non-signalling adversary.
Device independent quantum key distribution (QKD) aims to provide a higher degree of security than traditional QKD schemes by reducing the number of assumptions that need to be made about the physical devices used. The previous proof of security by Pironio et al (2009 New J. Phys. 11 045021) applies only to collective attacks where the state is identical and independent and the measurement devices operate identically for each trial in the protocol. We extend this result to a more general class of attacks where the state is arbitrary and the measurement devices have no memory. We accomplish this by a reduction of arbitrary adversary strategies to qubit strategies and a proof of security for qubit strategies based on the previous proof by Pironio et al and techniques adapted from Renner.
Device independent quantum key distribution (QKD) aims to provide a higher degree of security than traditional QKD schemes by reducing the number of assumptions that need to be made about the physical devices used. The previous proof of security by Pironio et al (2009 New J. Phys. 11 045021) applies only to collective attacks where the state is identical and independent and the measurement devices operate identically for each trial in the protocol. We extend this result to a more general class of attacks where the state is arbitrary and the measurement devices have no memory. We accomplish this by a reduction of arbitrary adversary strategies to qubit strategies and a proof of security for qubit strategies based on the previous proof by Pironio et al and techniques adapted from Renner.
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.
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.
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.