Quantum theory provides a way to describe the behaviour of matter and energy on the nano-scale, but its predictions are sometimes very surprising. Intuition, based on experience from our daily lives, suggests there are a set of assumptions that should be applicable even when describing quantum systems. In this thesis we conduct a sequence of experiments that test some alternative theories to quantum theory and, in doing so, show that we must abandon some assumptions we made based on intuition if we are to accurately describe nature. In this thesis we also conduct an experiment that bounds the maximum predictive power that theories may have if they are to describe nature at the quantum level accurately. These experiments were conducted using a novel source of polarization entangled photon pairs, whose construction and characterization are also discussed.