Tighter sum uncertainty relations via $(\hat{I}\pm ,{\hat{I}}^2,{\hat{I}}^3)$ weighted Wigner-Yanase-Dyson skew information

Abstract

We establish tighter uncertainty relations for arbitrary finite observables via $(\hat{I}\pm ,{\hat{I}}^2,{\hat{I}}^3)$ weighted Wigner-Yanase-Dyson ($(\hat{I}\pm ,{\hat{I}}^2,{\hat{I}}^3)$WWYD) skew information. The results are also applicable to the $(\hat{I}\pm ,{\hat{I}}^3)$ weighted Wigner-Yanase-Dyson ($(\hat{I}\pm ,{\hat{I}}^3)$WWYD) skew information and the weighted Wigner-Yanase-Dyson (WWYD) skew information. We also present tighter lower bounds of quantum channels and unitary channels via $(\hat{I}\pm ,{\hat{I}}^2,{\hat{I}}^3)$ modified weighted Wigner-Yanase-Dyson ($(\hat{I}\pm ,{\hat{I}}^2,{\hat{I}}^3)$MWWYD) skew information. Detailed examples are provided to illustrate tightness of our uncertainty relations.