Genuine multipartite Bell inequality for device-independent conference key agreement

Holz, Timo; Kampermann, Hermann; Bruß, Dagmar

doi:10.1103/physrevresearch.2.023251

Cited by 27 publications

(34 citation statements)

References 32 publications

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“…In Figure 5 we demonstrate that our technique can be used to recover the tight analytical bound [18] on inf H(A|X = 0, Q E ) for devices constrained to violate the Holz inequality [56] for three parties. Where the Holz inequality is formulated as follows: let Alice, Bob and Charlie each have binary input devices that give outputs in {1, −1}.…”

Section: The Npa Hierarchymentioning

confidence: 99%

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Device-independent lower bounds on the conditional von Neumann entropy

Brown¹,

Fawzi²,

Fawzi³

2021

Preprint

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The rates of several device-independent (DI) protocols, including quantum key-distribution (QKD) and randomness expansion (RE), can be computed via an optimization of the conditional von Neumann entropy over a particular class of quantum states. In this work we introduce a numerical method to compute lower bounds on such rates. We derive a sequence of optimization problems that converge to the conditional von Neumann entropy of systems defined on general separable Hilbert spaces. Using the Navascués-Pironio-Acín hierarchy we can then relax these problems to semidefinite programs, giving a computationally tractable method to compute lower bounds on the rates of DI protocols. Applying our method to compute the rates of DI-RE and DI-QKD protocols we find substantial improvements over all previous numerical techniques, demonstrating significantly higher rates for both DI-RE and DI-QKD. In particular, for DI-QKD we show a new minimal detection efficiency threshold which is within the realm of current capabilities. Moreover, we demonstrate that our method is capable of converging rapidly by recovering instances of known tight analytical bounds. Finally, we note that our method is compatible with the entropy accumulation theorem and can thus be used to compute rates of finite round protocols and subsequently prove their security.

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Section: The Npa Hierarchymentioning

confidence: 99%

“…Figure5: Recovering the tight analytical bound of[18]. Comparison of lower bounds on H(A|X = 0, Q E ) for quantum devices that constrained to achieve some minimal violation of the Holz inequality for three parties[56]. Numerical bounds were computed at a relaxation level 2 + ABC.…”

mentioning

confidence: 99%

Device-independent lower bounds on the conditional von Neumann entropy

Brown¹,

Fawzi²,

Fawzi³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…It has been generalized extensively to various cases including finite size [13], [14], continuous variables [15], [16] and four users with W state [17]. Moreover, the finite-key analysis with composable security [18], device independence [19], [20] and other special cases [21]- [23] are also considered in quantum CKA. The experimental demonstration of quantum CKA has been implemented recently over 50 km fiber using the state-of-the-art four-photon GHZ entanglement source [24].…”

Section: Introductionmentioning

confidence: 99%

High Key Rate Quantum Conference Key Agreement With Unconditional Security

Cao

Zhao

et al. 2021

IEEE Access

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Quantum cryptography is a major ingredient of the future quantum internet that promises various secure communication tasks. Quantum conference key agreement (CKA) is an important cryptographic primitive of quantum cryptography, which provides the conference key among multiple users simultaneously. However, quantum CKA is currently far from practical application due to the low conference key rate. Here, we propose a quantum CKA protocol of three users with information-theoretic security. Our protocol only requires phase-randomized weak coherent sources and threshold single-photon detectors, and is anticipated to be experimentally demonstrated over 600 km under current technology. Our scheme can be widely implemented in the approaching large-scale quantum network.

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“…As for the MABK-Bell function (2), the maximal violation value 2 (N −1)/2 appears if and only if for N -qubit Greenberger-Horne-Zeilinger (GHZ) states [10] or their local unitary equivalent partners [11]. Thus the Bell inequalities, not only can be designed as a nolocal game beaten via some quantum states outstriping any classical players (first shown in [12], and see also [13]), but act as a notable role in some quantum information processes [14], such as multipartite device-independent quantum key distribution [15], and ultraprecise metrology [16]. Considering their intriguing efficacy, and the difficulty to search for all Bell inequalities [17], it is necessary to find out a general iterative formula for Bell inequalities.…”

Section: Introductionmentioning

confidence: 99%

General Iterative Formulas of Bell's Inequalities

Fan¹,

Xu²,

Miao³

et al. 2021

Preprint

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Newton's second law aids us in predicting the location of a classical object after knowing its initial position and velocity together with the force it experiences at any time, which can be seen as a process of continuous iteration. When it comes to discrete problems, e.g. building Bell inequalities, as a vital tool to study the powerful nonlocal correlations in quantum information processing. Unless having known precisely the genereal formula of associated inequalities, iterative formulas build a bridge from simple examples to all elements in the set of Bell inequalities. Although exhaust all entities in the set, even in the subset of tight individuals, is a NP hard problem, it is possible to find out the evolution law of Bell inequalities from few-body, limited-setting and low-dimension situations to arbitrary (n, k, d) constructions, i.e. n particles, k measurements per particle, and d outcomes per measurement. In this work, via observing Śliwa's 46 tight (3,2,2) Bell inequalities [Phys. Lett. A. 317, 165-168 (2003)], uniting the "root" method [Phys. Rev. A. 79, 012115, (2009)] and the idea of degeneration, we discover an iterative formula of Bell inequalities containing all (n, k, 2) circumstances, which paves a potential way to study the current Bell inequalities in terms of iterative relations combining "root" method on the one hand, and explore more interesting inequalities on the other.

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Genuine multipartite Bell inequality for device-independent conference key agreement

Cited by 27 publications

References 32 publications

Device-independent lower bounds on the conditional von Neumann entropy

Device-independent lower bounds on the conditional von Neumann entropy

High Key Rate Quantum Conference Key Agreement With Unconditional Security

General Iterative Formulas of Bell's Inequalities

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