Example of lumped parameter modeling of a quantum optics circuit

Is it possible for a simple lumped parameter model of a circuit to yield correct quantum mechanical predictions of its behavior, when there is quantum entanglement between components of that circuit? This paper shows that it is possible in a simple but important example – the circuit of the original Bell’s Theorem experiments, for ideal polarizers. Correct predictions emerge from two alternative simple models, based on classical Markov Random Fields (MRF) across spacetime. Exact agreement with quantum mechanics does not violate Bell’s Theorem itself, because the interplay between initial and final outcomes in these calculations does not meet the classical definition of time-forwards causality. Both models raise interesting questions for future research. The final section discusses several possible directions for following up on these results, both in lumped system modeling and in more formal and general approaches. It describes how a new triphoton experiment, not yet performed, may be able to discriminate between MRF models and the usual measurement formalism of Copenhagen quantum mechanics.