Robust entanglement distribution via quantum network coding

Abstract

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.

A quantum network stack and protocols for reliable entanglement-based networks

“…There is extensive work on quantum networks relying on quantum repeaters [32,33,[36][37][38][39][40][41][42][43][44][45][46][47][48][49]. Most of these approaches have in common that they assume a network of quantum repeaters sharing Bell-pairs with each other.…”

“…On this layer, the techniques for establishing long-distance quantum communications reside. In particular, concrete technologies include quantum repeaters, bi- [28][29][30][31][32][33][34][36][37][38][39][40][41][42][43][44][45][46][47][48][49] or multipartite [57,76], but also the direct transmission of encoded quantum states [23][24][25][26] or percolation approaches [82,83] which generate entanglement structures in a noisy quantum network of networking devices by applying techniques from percolation theory. The main purpose of devices operating on this layer is to enable point-to-point or point-to-multipoint long-distance connectivity without any notion of requests.…”

“…A crucial element to establish long-distance entanglement are quantum repeaters [28][29][30][31][32][33][34][35], and multiple proposals for repeater-based networks have been put forward [32,33,[36][37][38][39][40][41][42][43][44][45][46][47][48][49]. Most schemes are based on bipartite entanglement, where Bell-pairs are generated between nodes of the network.…”

“…We also consider how to connect quantum routers in a hierarchical manner to reduce complexity, as well as reliability issues arising in connecting these quantum networking devices. quantum network shall not be limited to the generation of Bell-pairs only [50][51][52][53], because many interesting applications require multipartite entangled quantum states. Therefore, the ultimate goal of quantum networks should be to enable their clients to share arbitrary entangled states to perform distributed quantum computational tasks.…”

Structure of Multipartite Entanglement in Random Cluster-Like Photonic Systems

“…While the theory of quantum networks has found fertile applications in quantum communication [3] and ground-breaking results in the proposal of quantum repeaters for the faithful long-haul transport of quantum information [4,5], the implications of the emergence of small worlds have been far less explored, and mostly confined to studies of excitation-transport and the analysis of the transition from localised to delocalised regimes in spatially extended interacting-particle models [6,7].…”