Tighter uncertainty relations based on Wigner-Yanase skew information for observables and channels

Highlights: • Explore the sum uncertainty relations for observables based on skew information. • Explore the sum uncertainty relations for quantum channels based on skew information. • Present some new uncertainty relations for observables and quantum channels. • Our uncertainty relations have much tighter lower bounds than the existing ones. • Detailed examples are provided. Uncertainty principle is the basis of quantum mechanics. It reflects the basic law of the movement of microscopic particles. Wigner-Yanase skew information, as a measure of quantum uncertainties, is used to characterize the intrinsic features of the state and the observable. In this paper, we mainly investigate the sum uncertainty relations for both quantum mechanical observables and quantum channels based on skew information. We establish a new uncertainty relation in terms of skew information for n observables, which is saturated (thus it holds as equality) for two incompatible observables. We also present two uncertainty relations for arbitrary finite N quantum channels by using skew information. Our uncertainty relations have tighter lower bounds than the existing ones. Detailed examples are provided.