A note on uncertainty relations of metric-adjusted skew information

Abstract

The uncertainty principle is one of the fundamental features of quantum mechanics and plays a vital role in quantum information processing. We study uncertainty relations based on metric-adjusted skew information for finite quantum observables. Motivated by the paper [Physical Review A 104, 052414 (2021)], we establish tighter uncertainty relations in terms of different norm inequalities. Naturally, we generalize the method to uncertainty relations of metric-adjusted skew information for quantum channels and unitary operators. As both the Wigner-Yanase-Dyson skew information and the quantum Fisher information are the special cases of the metric-adjusted skew information corresponding to different Morozova-Chentsov functions, our results generalize some existing uncertainty relations. Detailed examples are given to illustrate the advantages of our methods.

14 pages, 3 figures

References in corpus (6)

• Stronger uncertainty relations for the sum of variances
• Entropic uncertainty relation for mutually unbiased bases
• Metric adjusted skew information
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Cited by in corpus (6)

• Tighter sum uncertainty relations via metric-adjusted skew information
• Summation and product forms of uncertainty relations based on metric-adjusted skew information
• Wigner-Yanase skew information-based uncertainty relations for quantum channels
• Uncertainty of quantum channels based on symmetrized \r{ho}-absolute variance and modified Wigner-Yanase skew information
• A note on Wigner-Yanase skew information-based uncertainty of quantum channels
• Uncertainty relations based on the $\rho$-absolute variance for quantum channels