Quantum linear network coding for entanglement distribution in restricted architectures

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. For a natural class of network codes, we showed how to realise such protocols as circuits in which each node is a single qubit, and also that classical control can be used to perform the protocols "out of order". This motivates our main result: that when a suitable linear network code exists, then it is possible to distribute entanglement with a quantum circuit of constant depth. To help prove this result, we developed a formalism that we term the QLNC formalism, which helps us to reason about QLNC circuits in general.