Research On Generalized Von Neumann Entropy And Quantum Discord In Bipartite Quantum Systems

The theory of quantum information is a combination of quantum information and quantum mechanics. Entropy is one of important concepts in the theory of quantum information, which is used to measure the uncertainty contained in the physical system. In this paper, we mainly introduce the generalized von Neumann entropy and the quantum discord in bipartite systems.In Chapter 1, we firstly introduce the research background and research status. Then, we list several basic definitions and theorems about Shannon entropy and von Neumann entropy which will be needed in the following two chapters.In Chapter 2, we firstly define the generalized von Neumann entropy, and then conduct a research on the properties and continuity of the generalized von Neumann entropy. We have proved that the generalized von Neumann entropy retained the partial properties of classical von Neumann entropy as follows:boundedness, con-cavity and Sf(ρA)=Sf(ρB) for a pure state ρAB in D(HA(?)HB), the other properties have changed. For the continuity of generalized von Neumann entropy, we let the function f satisfy:If there exits r∈(0,1), such that |f(x)-f(y)|≤f(|x-y|), x,y∈[0,1],|x-y|≤r (f(x)=xf(x)).Finally, we get the continuity and the uniform continuity of generalized von Neumann entropy.In Chapter 3, we made the unified-(q,s) entropy as a carrier to define the conditional entropy and mutual information for ρAB in D(HA(?)HB) before and after measurement, and then get the definition of quantum discord in bipartite systems.