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arXiv:1208.0023 · Physical Review X

Device-Independent Quantum Key Distribution with Local Bell Test

Charles Ci Wen Lim, Christopher Portmann, Marco Tomamichel, Renato Renner, Nicolas Gisin

Published Jul 30, 2013• 66 citations
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Abstract

Existing protocols for device-independent quantum key distribution solve the problem of inadvertently flawed devices, but still rely on two-party Bell tests across almost lossless quantum channels that are hard to realize over long distances. Now theorists propose a new device-independent protocol that allows Bell testing to be carried out by only one party, potentially enabling long-distance key distributions.

DOI
10.1103/physrevx.3.031006

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Existing protocols for device-independent quantum key distribution solve the problem of inadvertently flawed devices, but still rely on two-party Bell tests across almost lossless quantum channels that are hard to realize over long distances. Now theorists propose a new device-independent protocol that allows Bell testing to be carried out by only one party, potentially enabling long-distance key distributions.
Device-independent quantum key distribution (DIQKD) in its current design requires a violation of a Bell's inequality between two parties, Alice and Bob, who are connected by a quantum channel. However, in reality, quantum channels are lossy and current DIQKD protocols are thus vulnerable to attacks exploiting the detection loophole of the Bell test. Here, we propose a novel approach to DIQKD that overcomes this limitation. In particular, we propose a protocol where the Bell test is performed entirely on two casually independent devices situated in Alice's laboratory. As a result, the detection loophole caused by the losses in the channel is avoided.
Abstract Device-independent quantum key distribution (DIQKD) generates a secret key among two parties in a provably secure way without making assumptions about the internal working of the devices used in the protocol. The main challenge for a DIQKD physical implementation is that the data observed among the two parties must violate a Bell inequality without fair-sampling, since otherwise the observed correlations can be faked with classical resources and security can no longer be guaranteed. In spite of the advances recently made to achieve higher detection efficiencies in Bell experiments, DIQKD remains experimentally difficult at long distances due to the exponential increase of loss in the channel separating the two parties. Here we describe and analyze plausible solutions to overcome the crucial problem of channel loss in the frame of DIQKD physical implementations.
Device-independent quantum key distribution (DIQKD) provides a model of quantum key distribution with minimal assumptions and highly abstract theoretical building blocks. Although DIQKD frees us from detailed discussions of specific device models and associated error parameters, it replaces them with fundamental assumptions about the validity of quantum experiments. In this work, we propose a way to lift a protocol based on DIQKD-style assumptions to a device-dependent QKD protocol by performing local self-tests in the laboratories of the two key-generating parties. In particular, we consider routed Bell-test setups as a means of self-testing the local parties in earnest and develop a rigorous mathematical framework showing that the underlying optimization problems can indeed be transferred to the device-dependent QKD setting. As an application, we illustrate many of the relevant techniques through the case study of a routed BB84 protocol.
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.
One of the main challenges in device-independent quantum key distribution (DIQKD) is achieving the required Bell violation over long distances, as the channel losses result in low overall detection efficiencies. Recent works have explored the concept of certifying nonlocal correlations over extended distances through the use of a local Bell test. Here, an additional quantum device is placed in close proximity to one party, using short-distance correlations to verify nonlocal behavior at long distances. However, existing works have either not resolved the question of DIQKD security against active attackers in this setup, or used methods that do not yield tight bounds on the key rates. In this work, we introduce a general formulation of the key rate computation task in this setup that can be combined with recently developed methods for analyzing standard DIQKD. Using this method, we show that if the short-distance devices exhibit sufficiently high detection efficiencies, positive key rates can be achieved in the long-distance branch with lower detection efficiencies as compared to standard DIQKD setups. This highlights the potential for improved performance of DIQKD over extended distances in scenarios where short-distance correlations are leveraged to validate quantum correlations.
Device-independent quantum key distribution (DI-QKD) guarantees security with a minimal set of assumptions about the experimental setup. The challenge posed by its implementation could be tackled using routed Bell tests with entanglement swapping, or distant Bell state measurement (BSM) units. However, practical distances still require local tests with close-to-ideal violations or BSMs with high efficiency. We propose a DI-QKD protocol based on a multi-port BSM, and multiple sources and measurement devices, where in each round, routed tests are performed on randomly selected local devices. The violation of local Bell tests is checked even for the subset of rounds where successful BSM projections are achieved. By requiring that this violation remain consistent with the overall average, we specifically show improvements in the critical efficiencies of a three-port BSM, of up to 6%6\%6% in absolute terms for high visibilities. Without ideal violations, we also achieve arbitrarily small efficiencies with arbitrarily many BSM ports. Our approach enables long-distance DI-QKD, with access to highly efficient loophole-free routing setups, and multiple local tests (possibly imperfect) with very high local detection efficiencies. Remarkably, it avoids the use of quantum memories and the need for long-range Bell tests. Finally, we extend the concept of routing to dimension witnesses, where qubit-bounded sources send states to the BSM. This can be seen as a semi-device-independent extension of the aforementioned protocol.