  Quasi-particles are elementary excitations of condensed matter quantum
phases. Demonstrating that they keep quantum coherence while propagating is a
fundamental issue for their manipulation for quantum information tasks. Here,
we consider anyons, the fractionally charged quasi-particles 20 of the
Fractional Quantum Hall Effect occurring in two-dimensional electronic
conductors in high magnetic fields. They obey anyonic statistics, intermediate
between fermionic and bosonic. Surprisingly, anyons show large quantum
coherence when transmitted through the localized states of electronic
Fabry-P\'erot interferometers, but almost no quantum interference when
transmitted via the propagating states of Mach-Zehnder interferometers. Here,
using a novel interferometric 25 approach, we demonstrate that anyons do keep
quantum coherence while propagating. Performing two-particle time-domain
interference measurements sensitive to the two-particle Hanbury Brown Twiss
phase, we find 53% and 60% visibilities for anyons with charges e/5 and e/3.
Our results give a positive message for the challenge of performing controlled
quantum coherent braiding of anyons.
