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arXiv:2404.00792 · Physical Review Letters

Entropy Bounds for Device-Independent Quantum Key Distribution with Local Bell Test

Ernest Y.-Z. Tan, Ramona Wolf

Published Sep 19, 2024• 7 citations
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Abstract

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.

DOI
10.1103/physrevlett.133.120803

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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 (DIQKD) allows two distant parties to establish a secret key, based only on the observed Bell nonlocal distribution. It remains unclear, however, what the minimal resources for enabling DIQKD are and how to maximize the key rate from a given distribution. In the present Letter, we consider a scenario where several copies of a given quantum distribution are jointly processed via a local and classical wiring operation. We find that, under few assumptions, it is possible to activate device-independent key, that is, starting from a distribution that is useless in a DIQKD protocol, we obtain a positive asymptotic key rate by wiring several copies together. We coin this effect device-independent key activation. Our analysis focuses on the standard DIQKD protocol with one-way postprocessing, and we resort to semidefinite programming techniques for computing lower bounds on the key rate.
Photon losses are the main obstacle to fully photonic implementations of device-independent quantum key distribution (DIQKD). Motivated by recent work showing that routed Bell scenarios offer increased robustness to detection inefficiencies for the certification of long-range quantum correlations, we investigate DIQKD protocols based on a routed setup. In these protocols, in some of the test rounds, photons from the source are routed by an actively controlled switch to a nearby test device instead of the distant one. We show how to analyze the security of these protocols and compute lower bounds on the key rates using noncommutative polynomial optimization and the Brown-Fawzi-Fawzi method. We determine lower bounds on the asymptotic key rates of several simple two-qubit routed DIQKD protocols based on CHSH or BB84 correlations and compare their performance to standard protocols. For high-quality short-path tests, we find that routed DIQKD protocols are significantly more robust to losses, showing an improvement of approximately 30 % in the detection efficiency compared to their nonrouted counterparts. This translates to a large improvement in the distance over which nonzero key can be distilled in optical setups with near-perfect single-photon detectors, where the main source of loss in the setup is due to transmission in the fiber. Notably, the routed BB84 protocol achieves a positive key rate with a detection efficiency as low as 50 % for the distant device, the minimal threshold for any QKD protocol featuring two untrusted measurements. However, the advantages we find are highly sensitive to noise and losses affecting the short-range correlations involving the additional test device.
Device-independent quantum key distribution allows for proving the security of a shared cryptographic key between two distant parties with potentially untrusted devices. The security proof is based on the measurement outcome statistics (correlation) of a Bell experiment, and security is guaranteed by the laws of quantum theory. While it is known that the observed correlation must be Bell nonlocal in order to prove security, recent results show that Bell nonlocality is in general not sufficient for standard device-independent quantum key distribution. In this work, we show that conversely, there is no lower bound on the amount of nonlocality that is sufficient for device-independent quantum key distribution. Even more so, we show that from certain correlations that exhibit arbitrarily small nonlocality, one can still extract unbounded device-independent key rates. Therefore, a quantitative relation between device-independent key rates and Bell nonlocality cannot be drawn in general. Our main technique comprises a rigorous connection between self-testing and device-independent quantum key distribution, applied to a recently discovered family of Bell inequalities with arbitrarily many measurement outcomes.
Applications such as Device-Independent Quantum Key Distribution (DIQKD) require loophole-free certification of long-distance quantum correlations. However, these distances remain severely constrained by detector inefficiencies and unavoidable transmission losses. To overcome this challenge, we consider parallel repetitions of the recently proposed routed Bell experiments, where transmissions from the source are actively directed either to a nearby or a distant measurement device. We analytically show that the threshold detection efficiency of the distant device--needed to certify non-jointly-measurable measurements, a prerequisite of secure DIQKD--decreases exponentially, optimally, and robustly, following η∗=1/2Nη^*=1/2^Nη∗=1/2N, with the number NNN of parallel repetitions.
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.
Transmission loss represents a major obstacle to the device-independent certification of quantum correlations over long distances, limiting applications such as device-independent quantum key distribution (DIQKD). In this work, we investigate the recently proposed concept of routed Bell experiments, in which a particle sent to one side can be measured either near or far from the source. We prove that routed Bell tests involving only entangled qubits can certify quantum correlations even in the presence of arbitrary loss on the channel to the distant device. This is achieved by adapting concepts from self-testing and quantum steering to the routed Bell test framework. Finally, as a natural extension of our approach, we outline a DIQKD protocol that, in principle, is secure over arbitrary distances.