Note on the Wigner-Yanase-Dyson Skew Information

A generalization of Schrödinger’s uncertainty relation described by the Wigner–Yanase skew information

“…Motivated by the definition of the Wigner-Yanase skew information, Luo introduced the Wigner-Yanase correlation [3] for two observables A and B in any quantum state ρ as…”

“…In fact, there is no simple dominant relations between them. For example, for A, B ∈ S(H ), we know from [3] that the magnitude of the generalized covariance |Cov ρ |(A, B) may be larger or smaller than the generalized Wigner-Yanase correlation |Corr ρ |(A, B).…”

“…With the increasing interests in quantum information processing [2] and the foundations of quantum mechanics, the notion of skew information and its various derivations have been discussed by many authors [3][4][5][6][7]. Recall that for a density ρ ∈ D(H ) and an observable A, the WignerYanase skew information [8] is defined as…”

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

“…There are also many ways to describe uncertainty relations, such as entropy [3][4][5][6][7], variance [8][9][10][11] and majorization techniques [12][13][14][15]. In particular, the quantum uncertainty can also be characterized by skew information.…”

Sum uncertainty relations based on $(α,β,γ)$ weighted Wigner-Yanase-Dyson skew information

“…where [A, B] = AB − BA and ∆Ω = ψ|Ω 2 |ψ − ψ|Ω|ψ 2 is the standard deviation of an observable Ω. Many different characterizations and quantifications of quantum uncertainty have been proposed in terms of entropy [3][4][5][6][7][8][9][10][11], variance [12][13][14][15], under successive measurements [16][17][18][19], and with majorization techniques [9,[20][21][22].…”