Sum uncertainty relations for arbitrary $N$ incompatible observables

Abstract

We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty relations are explicitly derived. These bounds are shown to be tighter than the ones such as derived from the uncertainty inequality for two observables [Phys. Rev. Lett. 113, 260401 (2014)]. Detailed examples are presented to compare among our results with some existing ones.

10 pages

References in corpus (6)

• Heisenberg's Uncertainty Principle
• Stronger uncertainty relations for the sum of variances
• Sum Uncertainty Relation in Quantum Theory
• Rényi entropy uncertainty relation for successive projective measurements
• Characterization of quantum angular-momentum fluctuations via principal components
• Optimized entropic uncertainty relation for successive measurement