Sum uncertainty relations based on $(\alpha ,\beta ,\gamma )$ weighted Wigner-Yanase-Dyson skew information

Abstract

We introduce ($\alpha ,\beta ,\gamma$) weighted Wigner-Yanase-Dyson (($\alpha ,\beta ,\gamma$) WWYD) skew information and ($\alpha ,\beta ,\gamma$) modified weighted Wigner-Yanase-Dyson (($\alpha ,\beta ,\gamma$) MWWYD) skew information. We explore the sum uncertainty relations for arbitrary $N$ mutually noncommutative observables based on ($\alpha ,\beta ,\gamma$) WWYD skew information. A series of uncertainty inequalities are derived. We show by detailed example that our results cover and improve the previous ones based on the original Wigner-Yanase (WY) skew information. Finally, we establish new sum uncertainty relations in terms of the ($\alpha ,\beta ,\gamma$) MWWYD skew information for arbitrary $N$ quantum channels.

19 pages, 1 figure

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Cited by in corpus (5)

• Summation and product forms of uncertainty relations based on metric-adjusted skew information
• Quantifying coherence of quantum channels based on the generalized $\alpha$-$z$-relative Rényi entropy
• Tighter uncertainty relations based on $(\alpha ,\beta ,\gamma )$ modified weighted Wigner-Yanase-Dyson skew information of quantum channels
• Coherence monotones of quantum channels based on two generalized quantum relative entropies
• Uncertainty relations based on the $\rho$-absolute variance for quantum channels