Bounding the Quantum and Classical Resources in Bell Experiments

Bell's theory of nonlocality in quantum mechanics allows for interesting correlations between separated parties. In this scenario, both parties share a quantum state and measure it to obtain a classical value. Through entanglement, the results of the measurement from one party can affect the results of the other party's measurement. Quantum correlations reflect this idea as a probability distribution p(ab|xy) based on the measurements used (x for Alice and y for Bob) and the respective results obtained (a and b). In this thesis, we introduce an expression that limits what quantum states could be used to generate a given quantum correlation. This, in turn, yields a lower bound on the dimension needed for this quantum state. For a quantum correlation p(ab|xy), the dimension of the quantum state acts as a resource needed to generate it. Thus, having a bound on the dimension helps one to quantify the resources needed to generate a given correlation. In addition to quantum correlations, we adjust the bound to work with classical correlations as well, which are correlations generated using a shared probability distribution instead of a quantum state. We apply our quantum and classical bounds to well-studied correlations to test them based on known results and also generate randomly generated correlations to better understand their behavior. Finally, we report on our numerical findings.