Pfaffian formula for fermion parity fluctuations in a superconductor and application to Majorana fusion detection

Abstract

Kitaev's Pfaffian formula equates the ground-state fermion parity of a closed system to the sign of the Pfaffian of the Hamiltonian in the Majorana basis. Using Klich's theory of full counting statistics for paired fermions we generalize the Pfaffian formula to account for quantum fluctuations in the fermion parity of an open subsystem. A statistical description in the framework of random-matrix theory is used to answer the question when a vanishing fermion parity in a superconductor fusion experiment becomes a distinctive signature of an isolated Majorana zero-mode.