Quantum computation and quantum information
Quantum computation and quantum information
Complexity classification of network information flow problems
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Polynomial-Time Construction of Linear Network Coding
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
A constant bound on throughput improvement of multicast network coding in undirected networks
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Polynomial time algorithms for multicast network code construction
IEEE Transactions on Information Theory
Insufficiency of linear coding in network information flow
IEEE Transactions on Information Theory
On the capacity of information networks
IEEE Transactions on Information Theory
Nonreversibility and Equivalent Constructions of Multiple-Unicast Networks
IEEE Transactions on Information Theory
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This paper considers the problem of efficiently transmitting quantum states through a network. It has been known for some time that without additional assumptions it is impossible to achieve this task perfectly in general -- indeed, it is impossible even for the simple butterfly network. As additional resource we allow free classical communication between any pair of network nodes. It is shown that perfect quantum network coding is achievable in this model whenever classical network coding is possible over the same network when replacing all quantum capacities by classical capacities. More precisely, it is proved that perfect quantum network coding using free classical communication is possible over a network with k source-target pairs if there exists a classical linear (or even vector-linear) coding scheme over a finite ring. Our proof is constructive in that we give explicit quantum coding operations for each network node. This paper also gives an upper bound on the number of classical communication required in terms of k , the maximal fan-in of any network node, and the size of the network.