Mixedness in the Bell violation versus entanglement of formation - art. no. 044301

Recently, Munro. Nemoto. and White (The Bell Inequality:A Measure of Entang lement?, quant-ph/0102119) tried to indicate that the reason behind a state rho having a higher amount of entanglement (as quantified by the entanglem ent of formation) than a state rho', but producing the same amount of Bell violation, is due to the fact that the amount of mixedness (as quantified b y the linearized entropy) in rho is higher than that in rho'. We counter th eir argument with examples. We extend these considerations to the von Neuma nn entropy. Our results suggest that the reason as to why equal amount of B ell violation requires different amounts of entanglement cannot, at least, be explained by mixedness alone.