Asynchronous reference frame agreement in a quantum network

An efficient implementation of many multiparty protocols for quantum networks requires that all the nodes in the network share a common reference frame. Establishing such a reference frame from scratch is especially challenging in an asynchronous network where network links might have arbitrary delays and the nodes do not share synchronised clocks. In this work, we study the problem of establishing a common reference frame in an asynchronous network of $n$ nodes of which at most $t$ are affected by arbitrary unknown error, and the identities of the faulty nodes are not known. We present a protocol that allows all the correctly functioning nodes to agree on a common reference frame as long as the network graph is complete and not more than $t<n/4$ nodes are faulty. As the protocol is asynchronous, it can be used with some assumptions to synchronise clocks over a network. Also, the protocol has the appealing property that it allows any existing two-node asynchronous protocol for reference frame agreement to be lifted to a robust protocol for an asynchronous quantum network.