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

Abstract

We establish tighter uncertainty relations for arbitrary finite observables via (α, β, γ) weighted Wigner-Yanase-Dyson ((α, β, γ)WWYD) skew information. The results are also applicable to the (α, γ) weighted Wigner-Yanase-Dyson ((α, γ)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 (α, β, γ) modified weighted Wigner-Yanase-Dyson ((α, β, γ)MWWYD) skew information. Detailed examples are provided to illustrate tightness of our uncertainty relations.

Tighter uncertainty relations based on $(α,β,γ)$ modified weighted Wigner-Yanase-Dyson skew information of quantum channels

“…(a) q = 0.4; (b) q = 0.9. The above results show that Theorem 1 in this paper improve the existing results ones given in [27].…”

“…which is called the (α, γ) weighted Wigner-Yanase-Dyson ((α, γ) WWYD) skew information in [27]. Note that Eq.…”

“…( 2) when γ = 1 2 . We defined the (α, β, γ) weighted Wigner-Yanase-Dyson ((α, β, γ) WWYD) skew information as [27],…”

“…( 4) when β = 1 − α. We also defined the (α, β, γ) modified weighted Wigner-Yanase-Dyson ((α, β, γ) MWWYD) skew information with respect to a quantum state ρ and an arbitrary operator E (not necessarily Hermitian) in [27] as…”

Tighter sum uncertainty relations via (α, β, γ) weighted Wigner–Yanase–Dyson skew information

“…For arbitrary finite N observables A 1 , A 2 , L ,A N , Xu et al [34] provided the following sum uncertainty relations,…”