Interferometry of non-Abelian Anyons

TL;DR

This work develops a general quantum-measurement framework for non-Abelian anyons using interferometry, linking braiding data to readout of anyonic charge via monodromy quantities $M_{ab}$ and density-matrix evolution. It derives a comprehensive Mach-Zehnder interferometer theory for arbitrary anyon models, including all-order tunneling corrections, and analyzes how probe measurements collapse superpositions into fixed or rogue states, with large-$N$ asymptotics yielding clear, distinguishable charge sectors. The authors extend the approach to a fractional quantum Hall double point-contact interferometer and provide explicit predictions for Abelian hierarchy states, Moore–Read at $\nu=5/2$, and Read–Rezayi at $\nu=12/5$, highlighting practical readout implications for topological quantum computing. Overall, the paper connects interferometric observables to the underlying topological data ($F$- and $R$-symbols, $S$-matrix, monodromy) and outlines how to optimize measurements for reliable qubit initialization and topological order identification in realistic devices.

Abstract

We develop the general quantum measurement theory of non-Abelian anyons through interference experiments. The paper starts with a terse introduction to the theory of anyon models, focusing on the basic formalism necessary to apply standard quantum measurement theory to such systems. This is then applied to give a detailed analysis of anyonic charge measurements using a Mach-Zehnder interferometer for arbitrary anyon models. We find that, as anyonic probes are sent through the legs of the interferometer, superpositions of the total anyonic charge located in the target region collapse when they are distinguishable via monodromy with the probe anyons, which also determines the rate of collapse. We give estimates on the number of probes needed to obtain a desired confidence level for the measurement outcome distinguishing between charges, and explicitly work out a number of examples for some significant anyon models. We apply the same techniques to describe interferometry measurements in a double point-contact interferometer realized in fractional quantum Hall systems. To lowest order in tunneling, these results essentially match those from the Mach-Zehnder interferometer, but we also provide the corrections due to processes involving multiple tunnelings. Finally, we give explicit predictions describing state measurements for experiments in the Abelian hierarchy states, the non-Abelian Moore-Read state at $ν=5/2$ and Read-Rezayi state at $ν= 12/5$.

Figures (3)

• Figure 1: A Mach-Zehnder interferometer for an anyonic system. The target anyon(s) $A$ in the central region shares entanglement only with the anyon(s) $C$ outside this region. A beam of probe anyons $B_{1},\ldots ,B_{N}$ is sent through the interferometer, where $T_{j}$ are beam splitters, and detected at one of the two possible outputs by $D_{s}$.
• Figure 2: The transmission and reflection coefficients for a beam splitter.
• Figure 3: A double point-contact interferometer for measuring braiding statistics in fractional quantum Hall systems. The hatched region contains an incompressible FQH liquid. $S_s$ and $D_s$ indicate the "sources" and "detectors" of edge currents. The front gates (F) are used to bring the opposite edge currents (indicated by arrows) close to each other to form two tunneling junctions. Applying voltage to the central gate creates an antidot in the middle and controls the number $n$ of quasiholes contained there. An additional side gate (G) can be used to change the shape and the length of one of the paths in the interferometer.