Unitary Equivalence And Stability Entropy Of Quantum States

Entropy is one of the key concepts of quantum information theory and it pro-vides a method for measurement uncertainty contained in a information system. It has become a popular branch of quantum information theory with important re-search. This paper has some theories on the basis of research on the stability of entropy and the unitary equivalence of quantum states, the paper is divided into three chapters and the specifics are as follows:In chapter I, we introduce the symbols used in this paper and the relevant basic concepts and conclusions (such as majorization, entropy, separable state and so on). We obtain a very important relationship between majorization and entropy, i.e. if two vectors have the same entropy under the majorization condition, then the two vectors have the same elements.In chapter Ⅱ, we further study the relationship among majorization, entropy and separable state. we characterize the stability of entropy and study the stability of Shannon entropy and von Neumann entropy under the majorizationin relation. Moreover, we further research the structure of separable state and discusses in what condition the set{|(?)i〉} is orthogonal to each other. We also study the stability of entropy of the separable state.In Chapter III, we introduce the concept of the generalized quantum entropy and study the unitary equivalence of quantum states associated with the generalized quantum entropy by using the fundamental theorem. of algebra and the Vedic Newton theorem.