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\section{Introduction and Theory}  \par In their influential paper \cite{Einstein_1935}, Einstein, Podolsky, and Rosen (EPR) explored an ostensible paradox that arises from quantum mechanics. They concluded that quantum mechanics cannot be a complete theory, as it does not allow two non commuting operators and their physical quantities to have simultanous realities. Additionally, they rejected the possiblility of entanglement as described by quantum mechanics as being a realistic physical phenomena, and that though the physical prediction was correct, it could not be explained solely with quantum mechanical theories.  \par However, as Bell derived and others have demonstrated, it is possible to measure the correlation between two particles against Bell's inequality, thus showing the incompatibility of local hidden variable theory with physical reality. In our experiment, however, we followed Clauser, Horne, Shimony, and Holt (CHSH) \cite{Clauser_1969}, in which they derived a more practical way to measure the inequality by using photon polarization instead of electron spin.  \par Using this photon polarization basis, the value for the inequality is given by [3]  \[ S=E(a,b)-E(a,b^\prime)+E(a^\prime,b)+E(a^\prime,b^\prime) \]  \par where $(a,b,a^\prime,b^\prime)$ are polarization angles. The correlation between two angles is given by