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.