Characterization of quantum angular-momentum fluctuations via principal components

TL;DR

This paper introduces an SU(2) invariant method to analyze quantum angular-momentum fluctuations using covariance matrix diagonalization, providing new uncertainty relations applicable even when mean angular momentum is zero.

Contribution

It presents a novel, invariant approach to quantum angular-momentum fluctuations that simplifies analysis and derives meaningful uncertainty relations.

Findings

The method is SU(2) invariant and avoids commutator issues.

Derived nontrivial uncertainty relations for zero mean angular momentum.

Applied approach to relevant quantum states.

Abstract

We elaborate an approach to quantum fluctuations of angular momentum based on the diagonalization of the covariance matrix in two versions: real symmetric and complex Hermitian. At difference with previous approaches this is SU(2) invariant and avoids any difficulty caused by nontrivial commutators. Meaningful uncertainty relations are derived which are nontrivial even for vanishing mean angular momentum. We apply this approach to some relevant states.