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arXiv:quant-ph/0411209 · Physical Review A

Multipartite secure state distribution

Wolfgang Dür, John Calsamiglia, Hans J. Briegel

Published Apr 26, 2005• 39 citations
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Abstract

We introduce the distribution of a secret multipartite entangled state in a real-world scenario as a quantum primitive. We show that in the presence of noisy quantum channels (and noisy control operations), any state chosen from the set of two-colorable graph states (Calderbank-Shor-Steane codewords) can be created with high fidelity while it remains unknown to all parties. This is accomplished by either blind multipartite entanglement purification, which we introduce in this paper, or by multipartite entanglement purification of enlarged states, which offers advantages over an alternative scheme based on standard channel purification and teleportation. The parties are thus provided with a secret resource of their choice for distributed secure applications.

DOI
10.1103/physreva.71.042336

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We introduce the distribution of a secret multipartite entangled state in a real-world scenario as a quantum primitive. We show that in the presence of noisy quantum channels (and noisy control operations), any state chosen from the set of two-colorable graph states (Calderbank-Shor-Steane codewords) can be created with high fidelity while it remains unknown to all parties. This is accomplished by either blind multipartite entanglement purification, which we introduce in this paper, or by multipartite entanglement purification of enlarged states, which offers advantages over an alternative scheme based on standard channel purification and teleportation. The parties are thus provided with a secret resource of their choice for distributed secure applications.
We present a protocol in which two or more parties can share multipartite entanglement over noisy quantum channels. The protocol is based on the entanglement purification presented by Shor and Preskill [Phys. Rev. Lett. 85, 441 (2000)] and the quantum teleportation via an isotropic state. We show that a nearly perfect purification implies a nearly perfect sharing of multipartite entanglement between two parties so that the protocol can assure a faithful sharing of multipartite entanglement with Shor and Preskill's proof on the entanglement purification.
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.
We study the preparation and distribution of high-fidelity multiparty entangled states via noisy channels and operations. In the particular case of Greenberger-Horne-Zeilinger and cluster states, we study different strategies using bipartite or multipartite purification protocols. The most efficient strategy depends on the target fidelity one wishes to achieve and on the quality of transmission channel and local operations. We show the existence of a crossing point beyond which the strategy making use of the purification of the state as a whole is more efficient than a strategy in which pairs are purified before they are connected to the final state. We also study the efficiency of intermediate strategies, including sequences of purification and connection. We show that a multipartite strategy is to be used if one wishes to achieve high fidelity, whereas a bipartite strategy gives a better yield for low target fidelity.
In tasks where multipartite entanglement plays a central role, state purification is, due to inevitable noise, a crucial part of the procedure. We consider a scenario exploiting the multipartite entanglement in a straightforward multipartite purification algorithm and compare it to bipartite purification procedures combined with state teleportation. While complete purification requires an infinite amount of input states in both cases, we show that for an imperfect output fidelity the multipartite procedure exhibits a major advantage in terms of input states used.
We introduce a repeater scheme to efficiently distribute multipartite entangled states in a quantum network with optimal scaling. The scheme allows to generate graph states such as 2D and 3D cluster states of growing size or GHZ states over arbitrary distances, with a constant overhead per node/channel that is independent of the distance. The approach is genuine multipartite, and is based on the measurement-based implementation of multipartite hashing, an entanglement purification protocol that operates on a large ensemble together with local merging/connection of elementary building blocks. We analyze the performance of the scheme in a setting where local or global storage is limited, and compare it to bipartite and hybrid approaches that are based on the distribution of entangled pairs. We find that the multipartite approach offers a storage advantage, which results in higher efficiency and better performance in certain parameter regimes. We generalize our approach to arbitrary network topologies and different target graph states.
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.