Uncertainty principles on $C^{\ast }$-algebras

Abstract

In this paper we prove some uncertainty bounds for commutators and anti-commutators of observables in a $C^{\ast }$-algebra. We give a short, elementary proof of Robertson's Standard Uncertaity Principle in this setting. We also prove some other uncertainty relations for which the lower bound doesn't vanish for any number of observables.

11 pages, 0 figures