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

Abstract

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 Wigner-Yanase 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.

arXiv comment10 pages, 5 figures

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• Sum uncertainty relations based on $(\alpha ,\beta ,\gamma )$ weighted Wigner-Yanase-Dyson skew information
• Summation and product forms of uncertainty relations based on metric-adjusted skew information
• Tighter uncertainty relations based on $(\alpha ,\beta ,\gamma )$ modified weighted Wigner-Yanase-Dyson skew information of quantum channels
• Enhanced quantum channel uncertainty relations by skew information
• Parity symmetry breaking of spin-$j$ coherent state superpositions in Gaussian noise channel
• 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
• Uncertainty relation and the constrained quadratic programming