14,329 research outputs found
General Scheme for Perfect Quantum Network Coding with Free Classical Communication
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 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 , the maximal fan-in of any
network node, and the size of the network.Comment: 12 pages, 2 figures, generalizes some of the results in
arXiv:0902.1299 to the k-pair problem and codes over rings. Appeared in the
Proceedings of the 36th International Colloquium on Automata, Languages and
Programming (ICALP'09), LNCS 5555, pp. 622-633, 200
Directed percolation effects emerging from superadditivity of quantum networks
Entanglement indcued non--additivity of classical communication capacity in
networks consisting of quantum channels is considered. Communication lattices
consisiting of butterfly-type entanglement breaking channels augmented, with
some probability, by identity channels are analyzed. The capacity
superadditivity in the network is manifested in directed correlated bond
percolation which we consider in two flavours: simply directed and randomly
oriented. The obtained percolation properties show that high capacity
information transfer sets in much faster in the regime of superadditive
communication capacity than otherwise possible. As a byproduct, this sheds
light on a new type of entanglement based quantum capacity percolation
phenomenon.Comment: 6 pages, 4 figure
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