Summation and product forms of uncertainty relations based on metric-adjusted skew information

Uncertainty principle is one of the most essential features in quantum mechanics and plays profound roles in quantum information processing. We establish tighter summation form uncertainty relations based on metric-adjusted skew information via operator representation of observables, which improve the existing results. By using the methodologies of sampling coordinates of observables, we also present tighter product form uncertainty relations. Detailed examples are given to illustrate the advantages of our uncertainty relations.