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Quantum linear network coding as one-way quantum computation
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Network coding is a technique to maximize communication rates within a network, in communication protocols for simultaneous multi-party transmission of information. Linear network codes are examples of such protocols in which the local computations performed at the nodes in the network are limited to linear transformations of their input data (represented as elements of a ring, such as the integers modulo 2). The quantum linear network coding protocols of Kobayashi et al [arXiv:0908.1457 and arXiv:1012.4583] coherently simulate classical linear network codes, using supplemental classical communication. We demonstrate that these protocols correspond in a natural way to measurement-based quantum computations with graph states over over qudits [arXiv:quant-ph/0301052, arXiv:quant-ph/0603226, and arXiv:0704.1263] having a structure directly related to the network.
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Space-time Peer-to-Peer Distribution of Multi-party Entanglement for Any Quantum Network
A peer-to-peer protocol, P2PGSD, distributes arbitrary graph states over quantum networks, with hardness proofs and simulations showing up to 50% resource savings for sparse graphs.
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