Which States Violate Bell’s Inequality?

Bell’s inequality provides a theoretical test for local realism in nature. Experimental tests of this inequality have been carried out which show beyond reasonable doubt that local realism is incompatible with certain quantum states. What are the characteristics that set these states apart? I study the Clauser-Horne-Shimony-Holt (CHSH) inequality, a variation of Bell’s inequality, and outline my attempts to characterize the states which violate it. I discuss three methods and their associated difficulties: Symbolic manipulation using calculus, symbolic manipulation using linear algebra, and numerical solution using supercomputing resources.