Cumulants and the moment algebra: tools for analysing weak measurements

TL;DR

This paper introduces the moment algebra framework to simplify and generalize the analysis of multipartite weak measurements, including scenarios with thermal equilibrium, enhancing theoretical understanding and proof simplicity.

Contribution

It formulates the mathematical structure of cumulants in terms of the moment algebra, enabling easier proofs and broader applications in weak measurement scenarios.

Findings

Simplified analysis of multipartite weak measurements

Generalization to thermal equilibrium scenarios

Introduction of the moment algebra framework

Abstract

Recently it has been shown that cumulants significantly simplify the analysis of multipartite weak measurements. Here we consider the mathematical structure that underlies this, and find that it can be formulated in terms of what we call the moment algebra. Apart from resulting in simpler proofs, the flexibility of this structure allows generalizations of the original results to a number of weak measurement scenarios, including one where the weakly interacting pointers reach thermal equilibrium with the probed system.