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

## TL;DR

This paper generalizes Kitaev's Pfaffian formula to include quantum fluctuations in fermion parity for open systems, providing a statistical framework to identify Majorana zero-modes in superconductor experiments.

## Contribution

It extends the Pfaffian formula to open systems using full counting statistics, enabling better detection of Majorana zero-modes amidst quantum fluctuations.

## Key findings

- Generalized Pfaffian formula for open systems
- Statistical criteria for Majorana zero-mode detection
- Application to superconductor fusion experiments

## 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.