Braiding of anyonic quasiparticles in the charge transfer statistics of symmetric fractional edge-state Mach-Zehnder interferometer

We have studied the zero-temperature statistics of the charge transfer between the two edges of Quantum Hall liquids of, in general, different filling factors, ${\nu }_{0,1}=1\mathrm{/}(2m_{0,1}+1)$, with $m_0\ge m_1\ge 0$, forming Mach-Zehnder interferometer. General expression for the cumulant generating function in the large-time limit is obtained for symmetric interferometer with equal propagation times along the two edges between the contacts and constant bias voltage. The low-voltage limit of the generating function can be interpreted in terms of the regular Poisson process of electron tunneling, while its leading large-voltage asymptotics is proven to coincide with the solution of kinetic equation describing quasiparticle transitions between the $m$ states of the interferometer with different effective flux through it, where $m\equiv 1+m_0+m_1$. For $m>1$, this dynamics reflects both the fractional charge $e\mathrm{/}m$ and the fractional statistical angle $\pi \mathrm{/}m$ of the tunneling quasiparticles. Explicit expressions for the second (shot noise) and third cumulants are obtained, and their voltage dependence is analyzed.