Characterization of quantum angular-momentum fluctuations via principal components

Understand

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.