Bell Nonlocality And Local Hidden Variable Theory

The many differences between traditional classical physics and quantum mechanics provide excellent preconditions for the birth of many theories.Among them,Bell nonlocality,as a theoretical result of quantum mechanics,possesses rich theoretical research resources and thinking inspiration value.Starting from the EPR paradox,this thesis clarifies the conditions required for the local hidden variable model under the framework of classical physical thinking,and derives the Bell inequalities of the hidden variable model with translation invariance by combining mathematical tools and physical implications.Secondly,the many-body problems have always been of vital importance in physics,with the development of quantum information,the research value of many-body systems is becoming more and more prominent.This thesis explains various algorithms based on uniform matrix product states and explains the effectiveness of the Matrix Product States algorithm with the help of mathematical theory,and finally focuses on the Variational Uniform Matrix Product States algorithm and the Time-Dependent Vaiational Principle algorithm based on matrix product states.Finally,this thesis further explains the concept of contextuality by combining the above physical background and algorithmic tools,proposes a method that can verify the contextuality of one-dimensional infinite translational invariant hidden variable models,and performs numerical verification for three main types of models.Through data analysis and optimization,the results are finally found to verify contextuality,proving that the method proposed in this thesis is effective.At the same time,based on the various phenomena in the validation process,we provide development ideas for the direction of subsequent work such as high-dimensional extensions.