Tighter uncertainty relations based on $(\alpha ,\beta ,\gamma )$ modified weighted Wigner-Yanase-Dyson skew information of quantum channels

Abstract

We use a novel formation to illustrate the ($\alpha ,\beta ,\gamma$) modified weighted Wigner-Yanase-Dyson (($\alpha ,\beta ,\gamma$) MWWYD) skew information of quantum channels. By using operator norm inequalities, we explore the sum uncertainty relations for arbitrary $N$ quantum channels and for unitary channels. These uncertainty inequalities are shown to be tighter than the existing ones by a detailed example. Our results are also applicable to the modified weighted Wigner-Yanase-Dyson (MWWYD) skew information and the ($\alpha ,\gamma$) modified weighted Wigner-Yanase-Dyson (($\alpha ,\gamma$) MWWYD) skew information of quantum channels as special cases.

arXiv comment12 pages, 2 figures

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