Tensor network states for quantum foundations

Penrose developed a graphical language to reason about networks of connected tensors and applied these techniques to quantum theory. Here we present the development of a framework and tool set based on Penrose tensor networks that enables one to address certain questions of a foundational nature in quantum theory. A quantum tensor theory is one in which a fixed collection of tensors with clearly defined composition laws defines a physical theory. We show that each element of a universal collection of such tensors gives rise to a physical operation, allowed by the rules of quantum mechanics. Although each of these (possibly) atemporal operations is indeed physical, certain sequences of them could represent processes that violate the rules of quantum theory. The question is to determine when this is the case and we arrive at some perplexing conclusions.