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

Abstract

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