Spin-spin correlators in Majorana representation

TL;DR

This paper introduces an identity in the Majorana representation that simplifies the calculation of spin-spin correlators by relating them to one-particle fermionic correlators, aiding analysis of spin dynamics and measurements.

Contribution

It presents a novel identity linking spin-spin correlators to one-particle fermionic correlators in the Majorana representation, simplifying complex calculations.

Findings

Simplifies the calculation of spin-spin correlators

Enables analysis of spin dynamics in dissipative environments

Facilitates understanding of continuous quantum measurements

Abstract

In the Majorana representation of a spin 1/2 we find an identity which relates spin-spin correlators to one-particle fermionic correlators. This should be contrasted with the straightforward approach in which two-particle (four-fermion) correlators need to be calculated. We discuss applications to the analysis of the dynamics of a spin coupled to a dissipative environment and of a quantum detector performing a continuous measurement of a qubit's state.