Edge states and interferometers in the Pfaffian and anti-Pfaffian states of theν=52quantum Hall system

We compute the tunneling current in a double point contact geometry of a quantum Hall system at filling fraction $\nu =\frac{5}{2}$, as a function of voltage and temperature, in the weak tunneling regime. We quantitatively compare two possible candidates for the state at $\nu =\frac{5}{2}$: the Moore-Read Pfaffian state, and its particle-hole conjugate, the anti-Pfaffian. We find that both possibilities exhibit the same qualitative behavior, and both have an even-odd effect that reflects their non-Abelian nature, but differ quantitatively in their voltage and temperature dependence.