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Physical Review A

Efficiency bounds for testing a multiparticle Bell inequality in an asymmetric configuration

Wenchao Ma

Published Nov 15, 2023• 0 citations
Publisher

Abstract

Closing the fair sampling loophole in Bell-type experiments is crucial for a better understanding of the fundamentals of quantum mechanics and for realizing the security of quantum cryptography. However, an experimental demonstration of a Bell test without the fair sampling loophole is challenging. A central obstacle in photonic implementations is that the sampling efficiency, including the collection and detection efficiencies, must be above a certain threshold. We here investigate the minimum sampling efficiency for violating a multiparticle Bell inequality in an asymmetric configuration. The results show that the minimum sampling efficiency is arbitrarily close to $\frac{1}{n}$ in the $n$-particle system. Since the security of device-independent quantum key distribution (DI-QKD) protocols relies on the violation of a Bell inequality, we also investigate the application of the asymmetric Bell test in quantum cryptography. Based on the standard DI-QKD protocol, we demonstrate that the minimum sampling efficiency for extracting secure keys is reduced from $92.4%$ to $84.4%$. Therefore, we believe our work can serve as a recipe for experimentalists planning to implement DI-QKD.

DOI
10.1103/physreva.108.052216

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Closing the fair sampling loophole in Bell-type experiments is crucial for a better understanding of the fundamentals of quantum mechanics and for realizing the security of quantum cryptography. However, an experimental demonstration of a Bell test without the fair sampling loophole is challenging. A central obstacle in photonic implementations is that the sampling efficiency, including the collection and detection efficiencies, must be above a certain threshold. We here investigate the minimum sampling efficiency for violating a multiparticle Bell inequality in an asymmetric configuration. The results show that the minimum sampling efficiency is arbitrarily close to 1n\frac{1}{n}n1​ in the nnn-particle system. Since the security of device-independent quantum key distribution (DI-QKD) protocols relies on the violation of a Bell inequality, we also investigate the application of the asymmetric Bell test in quantum cryptography. Based on the standard DI-QKD protocol, we demonstrate that the minimum sampling efficiency for extracting secure keys is reduced from 92.492.4%92.4 to 84.484.4%84.4. Therefore, we believe our work can serve as a recipe for experimentalists planning to implement DI-QKD.
Abstract Bell’s inequality provides a remarkable way to test the consistency between quantum mechanics and classic local realistic theory. However, experimental demonstrations of the loophole-free Bell test are challenging and only recently have been demonstrated with bipartite systems. A central obstacle for the photonic system is that the sampling efficiency, including the collection and detection efficiencies, must be above a certain threshold. We here generalize two-particle Eberhard’s inequality to the n-particle systems and derive a Bell-type inequality for multi-particle systems, which significantly relaxes this threshold. Furthermore, an experimental proposal to achieve a multi-partite Bell test without the fair sampling assumption is presented for the case of three particles. For any given value of the sampling efficiency, we give the optimal configurations for actual implementation, the optimal state, the maximum background noise that the system can tolerate, and the lowest fidelity of the quantum state. We believe our work can serve as a recipe for experimentalists planning to violate local realism using a multi-partite quantum state without the sampling loophole.
Device-independent quantum key distribution (DI-QKD) offers the strongest form of security against eavesdroppers bounded by the laws of quantum mechanics. However, a practical implementation is still pending due to the requirement of combinations of visibility and detection efficiency that are beyond those possible with current technology. This mismatch motivates the search for DI-QKD protocols that can close the gap between theoretical and practical security. In this work, we present two DI-QKD protocols whose security relies on Bell inequalities with more than two inputs and two outputs. We show that, for maximally entangled states and perfect visibility, a protocol based on a Bell inequality with three inputs and four outputs requires a slightly lower detection efficiency than the protocols based on Bell inequalities with two inputs and two outputs.
Abstract We present a generic study on the information-theoretic security of multi-setting device-independent quantum key distribution (DIQKD) protocols, i.e. ones that involve more than two measurements (or inputs) for each party to perform, and yield dichotomic results (or outputs). The approach we develop, when applied in protocols with either symmetric or asymmetric Bell experiments, yields nontrivial upper bounds on the secure key rates, along with the detection efficiencies required upon the measuring devices. The results imply that increasing the number of measurements may lower the detection efficiency required by the security criterion. The improvement, however, depends on (i) the choice of multi-setting Bell inequalities chosen to be tested in a protocol, and (ii) either a symmetric or asymmetric Bell experiment is considered. Our results serve as an advance toward the quest for evaluating security and reducing efficiency requirement of applying DIQKD in scenarios without heralding.
Abstract The security of quantum key distribution (QKD) usually relies on that the users’s devices are well characterized according to the security models made in the security proofs. In contrast,device-independent QKD an entanglement-based protocol permits the security even without any knowledge of the underlying devices. Despite its beauty in theory, device-independent QKD is elusive to realize with current technology. This is because a faithful realization requires ahigh-quality violation of Bell inequality without the fair-sampling assumption. Particularly, in a photonic realization, a rather high detection efficiency is needed where the threshold values depend on the security proofs; this efficiency is far beyond the current reach. Here, both theoretical and experimental innovations yield the realization of device-independent QKD based on a photonic setup. On the theory side, to relax the threshold efficiency for practical deviceindependent QKD, we exploit the random post-selection combined with adding noise for preprocessing, and compute the entropy with complete nonlocal correlations. On the experiment side, we develop a high-quality polarization-entangled photonic source and achieve state-of-theart (heralded) detection efficiency of 87.49%, which outperforms previous experiments and satisfies the threshold efficiency for the first time. Together, we demonstrate device-independent QKD at a secret key rate of 466 bits/s over 20 m standard fiber in the asymptotic limit against collective attacks. Besides, we show the feasibility of generating secret keys at a fiber length of 220 meters. Importantly, our photonic implementation can generate entangled photons at a high rate and in the telecom wavelength, which is desirable for high-speed key generation over long distances. The results not only prove the feasibility of device-independent QKD with realistic devices, but also push the security of communication to an unprecedented level.
Abstract Device-independent quantum key distribution (DI-QKD) provides the gold standard for secure key exchange. Not only does it allow for information-theoretic security based on quantum mechanics, but it also relaxes the need to physically model the devices, thereby fundamentally ruling out many quantum hacking threats to which non-DI QKD systems are vulnerable. In practice though, DI-QKD is very challenging. It relies on the loophole-free violation of a Bell inequality, a task that requires high quality entanglement to be distributed between distant parties and close to perfect quantum measurements, which is hardly achievable with current technology. Notwithstanding, recent theoretical and experimental efforts have led to proof-of-principle DI-QKD implementations. In this article, we review the state-of-the-art of DI-QKD by highlighting its main theoretical and experimental achievements, discussing recent proof-of-principle demonstrations, and emphasizing the existing challenges in the field.
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.