Abstract
Many protocols of quantum information processing, like quantum key distribution or measurement-based 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. ). 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.
Highlights
Long distance quantum communication suffers from transmission losses
In this paper we described how graph state repeater with vertex degree larger than two, which we call quantum router, can employ network coding
It is well known that this measurement based quantum computation at intermediate network sites can increase the throughput of a network
Summary
Long distance quantum communication suffers from transmission losses. intermediate devices that recover the original signal, so-called quantum repeaters, are necessary [1, 2]. Many proposals for them have been made, including approaches based on repeat-untilsuccess strategies using two-way communication [3,4,5] and forward-error correction based protocols which do not require this acknowledgement of successful transmission [6,7,8,9]. In [17] we described a quantum repeater scheme based on quantum graph states [18, 19], which naturally generalizes to networks of such devices. Such a network consists of several parties connected by repeater lines according to a mathematical graph.
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