An uncertainty relation in terms of generalized metric adjusted skew information and correlation measure

The uncertainty principle in quantum mechanics is a fundamental relation with different forms, including Heisenberg’s uncertainty relation and Schrödinger’s uncertainty relation. In this paper, we prove a Schrödinger-type uncertainty relation in terms of generalized metric adjusted skew information and correlation measure by using operator monotone functions, which reads, $$\begin{aligned} U_\rho ^{(g,f)}(A)U_\rho ^{(g,f)}(B)\ge \frac{f(0)^2l}{k}\left| \mathrm {Corr}_\rho ^{s(g,f)}(A,B)\right| ^2 \end{aligned}$$Uρ(g,f)(A)Uρ(g,f)(B)≥f(0)2lkCorrρs(g,f)(A,B)2for some operator monotone functions f and g, all n-dimensional observables A, B and a non-singular density matrix $$\rho $$ρ. As applications, we derive some new uncertainty relations for Wigner–Yanase skew information and Wigner–Yanase–Dyson skew information.