Sum Uncertainty Relations Based on (α,β,γ) Weighted Wigner-Yanase-Dyson Skew Information

Abstract

We introduce (α,β,γ) weighted Wigner-Yanase-Dyson ((α,β,γ) WWYD) skew information and (α,β,γ) modified weighted Wigner-Yanase-Dyson ((α,β,γ) MWWYD) skew information. We explore the sum uncertainty relations for arbitrary N mutually noncommutative observables based on (α,β,γ) 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 (α,β,γ) MWWYD skew information for arbitrary N quantum channels.