Tighter uncertainty relations based on $(\hat{I}\pm ,{\hat{I}}^2,{\hat{I}}^3)$ modified weighted Wigner-Yanase-Dyson skew information of quantum channels

Abstract

We use a novel formation to illustrate the ($\hat{I}\pm ,{\hat{I}}^2,{\hat{I}}^3$) modified weighted Wigner-Yanase-Dyson (($\hat{I}\pm ,{\hat{I}}^2,{\hat{I}}^3$) 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 ($\hat{I}\pm ,{\hat{I}}^3$) modified weighted Wigner-Yanase-Dyson (($\hat{I}\pm ,{\hat{I}}^3$) MWWYD) skew information of quantum channels as special cases.

12 pages, 2 figures