On quantum network coding

We study the problem of error-free multiple unicast over directed acyclic networks in a quantum setting. We provide a new information-theoretic proof of the known result that network coding does not achieve a larger quantum information flow than what can be achieved by routing for two-pair communication on the butterfly network. We then consider a k-pair multiple unicast problem and for all k ≥ 2 we show that there exists a family of networks where quantum network coding achieves k-times larger quantum information flow than what can be achieved by routing. Finally, we specify a graph-theoretic sufficient condition for the quantum information flow of any multiple unicast problem to be bounded by the capacity of any sparsest multicut of the network. C © 2011 American Institute of Physics. [doi:10.1063/1.3555801]