Even-denominator fractional quantum Hall (FQH) states can be viewed as topological superconductors of composite fermions, supporting a charged chiral mode and $|{\mathcal{C}}_{cf}|$ neutral Majorana modes set by the Chern number ${\mathcal{C}}_{cf}$. Despite ongoing efforts, distinguishing the many competing paired phases remains an open problem. In this work, we propose a unified theory of charge transport across a quantum point contact for general paired FQH states described by an $\text{SO}{\left(N\right)}_1\times U\left(1\right)$ conformal field theory. We derive the boundary effective action for an arbitrary number of Majorana fermions $N=|{\mathcal{C}}_{cf}|$ and develop a nonperturbative instanton approximation to describe tunneling processes. We establish a weak-strong duality relating strong quasiparticle tunneling to weak electron tunneling. We calculate the scaling dimensions of the tunneling operators and demonstrate that while the weak-coupling fixed point is generally unstable, the strong-coupling fixed point is stable for physically relevant filling fractions and number of Majorana fermions. These transport exponents provide a distinct experimental fingerprint to identify the topological phases of even-denominator FQH states.

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• Anyons
• Edge states
• Fractional quantum Hall effect
• Majorana fermions
• Point contacts
• Bosonization
• Conformal field theory