Investigation On Violation Of CHSH Inequality By Entangled States With Continuous Variable

After Quantum Mechanics was founded, Einstein,Podolsky and Rosen has published an important article to declare that Quantum Mechanics was not self-contained in 1935, which is EPR Paradox as we know. It leads to the establishment of hidden variable theory. Bell quantitatively analysed whether hidden variable theory can represent the conclusions of Quantum Mechanics based on EPR Paradox and hidden variable theory by using classical statistics algorithm, this is Bell inequality as we know.The EPR Paradox has come ture since Bell has put forward express local hidden variable theory by using inequalities. But most of the outcome of the large amount of experiments was consilient to Quantum Mechanics, only a very small part of the experiments was consilient to Bell inequality. Bell inequality was generalized to many different forms by people afterwards. For example, GHZ Theory, Hardy inequality, Cabello inequality etc. The most original one is CHSH (Clauser-Horne-Shimony-Holt) inequality. Bell inequality open up an experiment research way to confirming the non-local attribute of Quantum Mechanics together with EPR Paradox.In this thesis, we retrospect the background and main relevance theory of Quantum Mechanics and Bell inequality and CHSH inequality. We choose the two particals entangled states with continuous variable to do the research on CHSH inequality. Since most of the research which demonstrate the Bell inequality was wrong use the dissociation variable quantum state. Here we use continuous variable quantum state to do our research. Entangled states with continuous variable has tremendous advantages in dealing with the quantum information. It has a very important purport in whether the theoretical or the experimental field. Since CHSH inequality was more symmetrical than Bell inequality, this will make our calculation more convenience comparatively. Here in this thesis we should observe the variational trend of the maximum violation of CHSH inequality which is depend on the continuous variable. Then we will add three kinds of noise into the two particals entangled states with continuous variable. Generally speaking, noise should be treat as a composition of several kinds of overturned errors. As a matter of convenience, here we use three kinds of overturned errors:bit overturned errors, phase overturned errors and bit-phase overturned errors. We will observe the variational of the two particals entangled states with continuous variable which was added in noise, we will also calculate the variational of the maximum violation of CHSH inequality after we add noise in which will depend on continuous variable and the probability of the noise was added.