Tighter sum uncertainty relations via metric-adjusted skew information

Abstract

In this paper, we first provide three general norm inequalities, which are used to give new uncertainty relations of any finite observables and quantum channels via metric-adjusted skew information. The results are applicable to its special cases as Wigner-Yanase-Dyson skew information. In quantifying the uncertainty of channels, we discuss two types of lower bounds and compare the tightness between them, meanwhile, a tight lower bound is given. The uncertainty relations obtained by us are stronger than the existing ones. To illustrate our results, we give several specific examples.

17 pages, 4 figures

References in corpus (6)

• Stronger uncertainty relations for the sum of variances
• Formulation of the uncertainty relations in terms of the Renyi entropies
• Metric adjusted skew information
• True precision limits in quantum metrology
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Cited by in corpus (5)

• Enhanced quantum channel uncertainty relations by skew information
• Parameterized Multi-observable Sum Uncertainty Relations
• 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