Abstract

In this talk I’ll present our recent paper on quantum linear network coding (arXiv 1910.03315). Our results build on previous work showing that linear network coding protocols can be applied to the problem of entanglement distribution over quantum networks – in particular distributing Bell pairs between pairs of “transmitter” and “receiver” nodes. We noticed two important features – that such quantum linear network coding (QLNC) protocols can be executed when each node is a single qubit, and that classical control can be used to perform the protocols “out of order” – which motivated our main result: that if a linear network code exists, then it is possible to distribute entanglement with a quantum circuit of constant depth. To prove this result, we proposed a formalism that we term the QLNC formalism, which helps us to reason about QLNC circuits in general.