Constructing Quantum Network Coding Schemes from Classical Nonlinear Protocols

Understand

The k-pair problem in network coding theory asks to send k messages simultaneously between k source-target pairs over a directed acyclic graph.

• In a previous paper [ICALP 2009, Part I, pages 622--633] the present authors showed that if a classical k-pair problem is solvable by means of a linear coding scheme, then the quantum k-pair problem over the same graph is also solvable, provided that classical communication can be sent for free between any pair of nodes of the graph.
• Here we address the main case that remained open in our previous work, namely whether nonlinear classical network coding schemes can also give rise to quantum network coding schemes.
• This question is motivated by the fact that there are networks for which there are no linear solutions to the k-pair problem, whereas nonlinear solutions exist.