-The effect of turbulence on entanglementbased free-space quantum key distribution with photonic orbital angular momentum Sandeep K Goyal, Alpha Hamadou Ibrahim, Filippus S Roux et al. - Recent citationsSemi-device-independent multiparty quantum key distribution in the asymptotic limit Yonggi Jo and Wonmin Son AbstractThe 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.In the quantum world, randomness and security are built-in properties [1][2][3]: two parties may establish a random secret key by exploiting the no-cloning theorem [4], as in the BB84 protocol [5], or by using the monogamy of entanglement [6], as in the Ekert protocol [7]. Several variations of these seminal protocols have been suggested [8][9][10][11][12], and their security has been analysed in detail [13][14][15][16][17][18][19].In the advent of quantum technologies, much effort is devoted to building quantum networks [20][21][22][23][24][25] and creating global quantum states across them [26,27]. Thus, the generalisation of quantum key distribution (QKD) to multipartite scenarios is topical. In order to establish a common secret key (the conference key) for N parties, one can follow mainly two different paths: building up the multipartite key from bipartite QKD links (2QKD) [28], see figure 1(a), or exploiting correlations of genuinely multipartite entangled states (NQKD) [29][30][31][32], see figure 1(b).In this article we devise a protocol based on the Greenberger-Horne-Zeilinger (GHZ) state and three measurement settings per party. While, for reasons discussed below, previous work also uses the GHZ state, the measurements differ. We provide an information theoretic security analysis of our NQKD protocol, by generalising methods developed for 2QKD in [16,33], and perform an analytical calculation of secret key rates. To the best of our knowledge this is the first explicit key rate calculation for multipartite QKD. This enables us to quantitatively compare the two approaches; we find that NQKD may outperform 2QKD, for example in networks with bottlenecks.The article is structured as follows. In the section 1 we introduce the NQKD protocol and its prepare-andmeasure variant, perform a detailed security analysis and the secret key rate calculation. In section 2 we define the 2QKD protocol, summarise the steps of the NQKD protocol in an implementation and calculate the secret key rate for the example...

Society relies and depends increasingly on information exchange and communication. In the quantum world, security and privacy is a built-in feature for information processing. The essential ingredient for exploiting these quantum advantages is the resource of entanglement, which can be shared between two or more parties. The distribution of entanglement over large distances constitutes a key challenge for current research and development. Due to losses of the transmitted quantum particles, which typically scale exponentially with the distance, intermediate quantum repeater stations are needed. Here we show how to generalise the quantum repeater concept to the multipartite case, by describing large-scale quantum networks, i.e. network nodes and their long-distance links, consistently in the language of graphs and graph states. This unifying approach comprises both the distribution of multipartite entanglement across the network, and the protection against errors via encoding. The correspondence to graph states also provides a tool for optimising the architecture of quantum networks. IntroductionQuantum entanglement is one of the pillars of quantum information processing. Distribution of entanglement among two or more spatially separated parties is a necessary ingredient for many tasks in quantum information theory, including distributed quantum computing [1], blind quantum computing [2], teleportation [3], telecloning [4], secret sharing [5] and quantum cryptography schemes [6][7][8]. Multipartite entanglement enables a violation of Bell inequalities that grows exponentially with the number of parties [9]. However, the controlled distribution of entanglement, in particular of multipartite entanglement, over long distances is a major challenge, due to unavoidable imperfections such as particle losses and decoherence.The seminal idea of quantum repeaters [10, 11] is based on the distribution of short-range entanglement between intermediate repeater stations (thus avoiding losses that grow typically exponentially with the distance) and subsequent entanglement swapping, which connects the short links along a line to long-range bipartite entanglement. Several theoretical variations have been proposed: some of them are based on entanglement distillation [12][13][14] and others are based on forward error correction [15][16][17][18]. Much experimental progress towards the realisation of a quantum repeater has been made [19][20][21][22][23][24][25].'Partially quantum' networks are considered in the so-called trusted node scenario [26], while fully quantum networks have been investigated in the context of network routing [27][28][29][30] and coding [31-33] strategies and heterogeneous network technologies [34].Here we propose a general multipartite quantum network architecture, where the long-distance links are bridged by quantum repeater stations. This idea is illustrated in figure 1 for the long-term vision of a 'world-wide quantum web'. This network contains nodes (labelled by letters), which receive, measure and send pa...

Many protocols of quantum information processing, like quantum key distribution or measurementbased quantum computation, 'consume' entangled quantum states during their execution. When participants are located at distant sites, these resource states need to be distributed. Due to transmission losses quantum repeater become necessary for large distances (e.g. 300 km). Here we generalize the concept of the graph state repeater to D-dimensional graph states and to repeaters that can perform basic measurement-based quantum computations, which we call quantum routers. This processing of data at intermediate network nodes is called quantum network coding. We describe how a scheme to distribute general two-colourable graph states via quantum routers with network coding can be constructed from classical linear network codes. The robustness of the distribution of graph states against outages of network nodes is analysed by establishing a link to stabilizer error correction codes. Furthermore we show, that for any stabilizer error correction code there exists a corresponding quantum network code with similar error correcting capabilities.

We present a simple analytic bound on the quantum value of general correlation type Bell inequalities, similar to Tsirelson's bound. It is based on the maximal singular value of the coefficient matrix associated with the inequality. We provide a criterion for tightness of the bound and show that the class of inequalities where our bound is tight covers many famous examples from the literature. We describe how this bound helps to construct Bell inequalities, in particular inequalities that witness the dimension of the measured observables.

Losses of optical signals scale exponentially with the distance. Quantum repeaters are devices that tackle these losses in quantum communication by splitting the total distance into shorter parts. Today two types of quantum repeaters are subject of research in the field of quantum information: Those that use two-way communication and those that only use one-way communication. Here we explain the details of the performance analysis for repeaters of the second type. Furthermore we compare the two different schemes. Finally we show how the performance analysis generalizes to large-scale quantum networks.Comment: 13 pages, 9 figures, 5 table