I have some questions about this paper: http://arxiv.org/abs/1102.1994v2 The author computes the entropy of the classical simulator using the Shannon entropy, then computes the entropy of the quantum simulator using von Neumann entropy and gets a smaller number, thus concluding that quantum simulators require smaller input. Firstly, are these two measures directly comparable? For example, the von Neumann entropy of a pure state is 0, even if it's maximally entangled. The corresponding classical entropy would be nonzero (and maximized). Also, it doesn't seem like the quantum simulator is using any less internal memory. It still seems to require log(|S|) qubits (S = space of causal states), which is the same internal memory as the classical model.