Fractional quantum Hall (FQH) states are highly sought after because of their ability to host non-Abelian anyons, whose braiding statistics make them excellent candidates for qubits in topological quantum computing. Multiple theoretical studies on the $\nu =\frac{12}{5}$ FQH state predict various quasiparticle states hosted by the $\frac{12}{5}$ plateau, which include ${\mathbb{Z}}_3$ parafermions and Majorana modes. In this work, we provide a systematic protocol to distinguish among four possible candidate wavefunctions of the $\frac{12}{5}$ plateau using zero-frequency shot noise experiments on a filter geometry. Qualitative comparisons of Fano factors provide a robust way to predict the candidate state across both the full and partial thermal equilibration regimes without prior knowledge of the experimental information, such as thermal equilibration length, allowing for more realistic experiments.

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• Edge states
• Fractional quantum Hall effect
• Shot noise
• Topological order