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

Abstract

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.

References in corpus (8)

• Metric adjusted skew information
• Majorization approach to entropic uncertainty relations for coarse-grained observables
• Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures
• Uncertainty of quantum channels via modified generalized variance and modified generalized Wigner-Yanase-Dyson skew information
• Uncertainty Relations Based on Modified Wigner-Yanase-Dyson Skew Information
• A note on uncertainty relations of metric-adjusted skew information
• Uncertainty and complementarity relations based on generalized skew information
• Sum uncertainty relations based on $(\alpha ,\beta ,\gamma )$ weighted Wigner-Yanase-Dyson skew information

Cited by in corpus (1)

• Uncertainty of quantum channels based on symmetrized \r{ho}-absolute variance and modified Wigner-Yanase skew information