Characterization of quantum angular-momentum fluctuations via principal components

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.

10 pages, Two column. New section II and some clarifying comments

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• Not all pure entangled states are useful for sub shot-noise interferometry
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• Tighter Uncertainty and Reverse Uncertainty Relations
• Weighted Uncertainty Relations
• Nonclassicality of states and measurements by breaking classical bounds on statistics
• Variance uncertainty relations without covariances for three and four observables
• State-independent preparation uncertainty relations
• Improving sum uncertainty relations with the quantum Fisher information
• SU(2)-invariant depolarization of quantum states of light
• State independent uncertainty relations from eigenvalue minimization
• SU(2) uncertainty limits
• Quantum Polarimetry
• Practical schemes for the measurement of angular-momentum covariance matrices in quantum optics
• Angular-momentum nonclassicality by breaking classical bounds on statistics
• A note on Wigner-Yanase skew information-based uncertainty of quantum channels
• Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems
• Sum uncertainty relations for arbitrary $N$ incompatible observables
• Quantum Uncertainty and Entropy