Some Research About Skew Information Of The Bounded Linear Operator

Quantum mechanics is one of the pillars of modern physics theory. The famous physicists Winger and Yanase in the study of quantum measurement theory puts forward the concept of quantum information theory. Based on the quantum infor-mation theory on the basis of applying the idea of algebra, analysis method, study the generalized Wigner-Yanase-Dyson skew information with two parameters and its related properties, also gives the self-adjoint operator’s skew information, vari-ance, covariance and correlation measure under two systems, and compared with one system. Finally, research the skew information’s additivity related issues.This article is divided into three chapters and arranged as follows:In Chapter 1, we introduce some research background and status on our main contents,definitions and theorems.In Chapter 2, we first introduce the two parameter extensions of the Wigner-Yanase-Dyson skew information’s definition; then we discuss some properties of this generalization of the Wigner-Yanase-Dyson skew information. Finally, we give the generalization of the Schrodinger uncertainty relation and the proof.In Chapter 3,we study the skew information, variance, covariance and corre-lation measure in two systems when self-adjoint operator, and compare them with when they are in one system. Firstly, we study the definitions of skew information, variance, covariance and correlation measure. Secondly, we introduce the additiv-ity and proof, also we give a conjecture and an example. Finally, we study the additivity of skew information when density operator is either self-adjoint or not self-adjoint.