Print Email Facebook Twitter Bell inequalities and their maximal violation Title Bell inequalities and their maximal violation Author Veerkamp, K. (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Applied Sciences) Contributor Caspers, M.P.T. (mentor) Elkouss Coronas, D. (mentor) Gijswijt, D.C. (graduation committee) Terhal, B.M. (graduation committee) Degree granting institution Delft University of Technology Programme Applied Mathematics | Applied Physics Date 2020-07-10 Abstract Bell inequalities are certain probabilistic inequalities that should hold in the context of quantum measurement under assumption of a local hidden variable model. These inequalities can be violated according to the theory of quantum mechanics and have also been violated experimentally. Bell inequalities were therefore historically used to disprove local hidden variable models as an interpretation of quantum mechanics. An interesting question is to what degree Bell inequalities can be violated according to the theory of quantum mechanics. The degree to which a particular Bell inequality can be violated is quantified by the largest violation of the Bell inequality. A central question we address in this thesis is how large the largest violation can become when considering all possible Bell inequalities. In particular the CHSH-inequality, a well-known Bell inequality, has a largest violation equal to the square root of 2 and we want to find a Bell inequality with largest violation exceeding the square root of 2. This thesis consists of two main parts. In the first part we formally define Bell inequalities and the largest violation and prove several theorems about Bell inequalities. In the second part we search for Bell inequalities with largest violation exceeding the square root of 2. We do this by first approximating the largest violation of a given Bell inequality using numerical optimization. Next, using this approximation, we use numerical optimization to maximize the largest violation. Due to run-time restrictions we were only able to consider Bell inequalities with a relatively small number of terms and were unable to find any among them with largest violation exceeding the square root of 2. Subject Bell inequalitiesviolationquantum measurementCHSH-inequality To reference this document use: http://resolver.tudelft.nl/uuid:2f3380d4-a66a-4389-b4d0-f330bf352592 Part of collection Student theses Document type bachelor thesis Rights © 2020 K. Veerkamp Files PDF BEP_Bell_inequalities_fin ... _2020_.pdf 614.94 KB Close viewer /islandora/object/uuid:2f3380d4-a66a-4389-b4d0-f330bf352592/datastream/OBJ/view