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arXiv:1612.05585 · New Journal of Physics

Multi-partite entanglement can speed up quantum key distribution in networks

Michael Epping, Hermann Kampermann, Chiara Macchiavello, Dagmar Bruß

Published Sep 14, 2017• 206 citations
arXivHTMLPDF

Abstract

The laws of quantum mechanics allow for the distribution of a secret random key between two parties.Here we analyse the security of a protocol for establishing a common secret key between N parties (i.e. a conference key), using resource states with genuine N-partite entanglement.We compare this protocol to conference key distribution via bipartite entanglement, regarding the required resources, achievable secret key rates and threshold qubit error rates.Furthermore we discuss quantum networks with bottlenecks for which our multipartite entanglement-based protocol can benefit from network coding, while the bipartite protocol cannot.It is shown how this advantage leads to a higher secret key rate. Multipartite QKD: protocol and security analysisThe entanglement-based Ekert protocol [7] can be generalised to N parties as follows, see also [31,34].The parties A and B 1 , B 2 , ..., B N 1 -share an N-partite entangled state and perform local projective measurements.The

DOI
10.1088/1367-2630/aa8487

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The laws of quantum mechanics allow for the distribution of a secret random key between two parties.Here we analyse the security of a protocol for establishing a common secret key between N parties (i.e. a conference key), using resource states with genuine N-partite entanglement.We compare this protocol to conference key distribution via bipartite entanglement, regarding the required resources, achievable secret key rates and threshold qubit error rates.Furthermore we discuss quantum networks with bottlenecks for which our multipartite entanglement-based protocol can benefit from network coding, while the bipartite protocol cannot.It is shown how this advantage leads to a higher secret key rate. Multipartite QKD: protocol and security analysisThe entanglement-based Ekert protocol [7] can be generalised to N parties as follows, see also [31,34].The parties A and B 1 , B 2 , ..., B N 1 -share an N-partite entangled state and perform local projective measurements.The
Secret sharing is a multiparty cryptographic primitive that can be applied to a network of partially distrustful parties for encrypting data that is both sensitive (it must remain secure) and important (it must not be lost or destroyed).When sharing classical secrets (as opposed to quantum states), one can distinguish between protocols that leverage bipartite quantum key distribution (QKD) and those that exploit multipartite entanglement.The latter class are known to be vulnerable to so-called participant attacks and, while progress has been made recently, there is currently no analysis that quantifies their performance in the composable, finite-size regime, which has become the gold standard for QKD security.Given this-and the fact that distributing multipartite entanglement is typically challenging-one might well ask is there any virtue in pursuing multipartite entanglement-based schemes?Here, we answer this question in the affirmative for a class of secret-sharing protocols based on continuous-variable graph states.We establish security in a composable framework and identify a network topology, specifically a bottleneck network of lossy channels, and parameter regimes within the reach of present-day experiments for which a multipartite scheme outperforms the corresponding QKD-based method in the asymptotic and finite-size setting.Finally, we establish experimental parameters where the multipartite schemes outperform any possible QKD-based protocol.This is one of the first concrete compelling examples of multipartite entangled resources achieving a genuine advantage over point-to-point protocols for quantum communication and represents a rigorous, operational benchmark to assess the usefulness of such resources.
We analyze the security of two multipartite quantum key distribution (QKD) protocols, specifically we introduce an N -partite version of the BB84 protocol and we discuss the N -partite six-state protocol proposed by Epping et al (2017 New J. Phys. 19 093012). The security analysis proceeds from the generalization of known results in bipartite QKD to the multipartite scenario, and takes into account finite resources. In this context we derive a computable expression for the achievable key rate of both protocols by employing the best-known strategies: the uncertainty relation and the postselection technique. We compare the performances of the two protocols both for finite resources and infinitely many signals.
The development of large-scale quantum communication networks necessitates the efficient distribution of quantum states to enable advanced cryptographic applications and distributed tasks. Multipartite entanglement is a key resource in many of these proposals, yet its generation is experimentally challenging, especially in noisy and lossy networks. While a substantial body of work focuses on the distribution of multi-partite entanglement in star-like topologies, practical implementations often rely on linear network structures constrained by existing infrastructure. In this work, we investigate the generation of high-fidelity multipartite entangled states in a realistic quantum network, leveraging the existing infrastructure of the Q-net-Q project-a real-world long-distance link connecting Berlin and Frankfurt via seven trusted relay nodes. Given that only bipartite entanglement sources are available in our setting and that the network is highly lossy, we explore the role of quantum memories in enhancing multi-partite entanglement distribution and identify key performance requirements. Furthermore, we analyze the feasibility and performance of cryptographic primitives-including (Anonymous) Conference Key Agreement and Quantum Secret Sharing-highlighting the scenarios where the use of multipartite entanglement yields clear advantages.
Abstract Conference key agreement (CKA), or multipartite key distribution, is a cryptographic task where more than two parties wish to establish a common secret key. A composition of bipartite quantum key distribution protocols can accomplish this task. However, the existence of multipartite quantum correlations allows for new and potentially more efficient protocols, to be applied in future quantum networks. Here, the existing quantum CKA protocols based on multipartite entanglement are reviewed, both in the device‐dependent and the device‐independent scenario.
Abstract Quantum conference key agreement (QCKA) allows multiple users to establish a secure key from a shared multi-partite entangled state. In a quantum network, this protocol can be efficiently implemented using a single copy of a N-qubit Greenberger-Horne-Zeilinger (GHZ) state to distil a secure N-user conference key bit, whereas up to N-1 entanglement pairs are consumed in the traditional pair-wise protocol. We demonstrate the advantage provided by GHZ states in a testbed consisting of a photonic six-user quantum network, where four users can distil either a GHZ state or the required number of Bell pairs for QCKA using network routing techniques. In the asymptotic limit, we report a more than two-fold enhancement of the conference key rate when comparing the two protocols. We extrapolate our data set to show that the resource advantage for the GHZ protocol persists when taking into account finite-key effects.
Future quantum communication networks will conceivably support cryptographic tasks that require entanglement among more than two users. Quantum secret sharing is a prime example where entanglement provides a direct means to coordinate untrusted parties with security from eavesdropping in a multi-party setting. However, the canonical GHZ-based protocols can be vulnerable to participant attacks, in which untrusted parties try to learn the secret without collaborating. Here, we experimentally evaluate a discrete-variable (n,n)(n,n)(n,n)-threshold quantum secret-sharing protocol whose finite-key analysis provides composable security against general attacks, including participant attacks. Using two domain-engineered entangled photon pair sources, we generate 4-qubit GHZ states at rates above 5×1035\times10^35×103 fourfold events per second and a maximum asymptotic secret key rate of 750±10750 \pm 10750±10 bits per second. We then distribute the state through a 4-arm star network comprising 20km of fibre in total. From the measured event rates and error statistics, we infer that a randomised 24-hour execution with the optimised basis probability would yield a composable finite-key lower bound of 8.7 Mbits, under the assumption that the measured source and device statistics remain stationary.