Mixedness in the Bell violation versus entanglement of formation
Sibasish Ghosh, Guruprasad Kar, Aditi Sen, Ujjwal Sen · Physical Review A · 2001
Recently, Munro, Nemoto, and White (The Bell Inequality: A Measure of Entanglement?, quant-ph/0102119) tried to indicate that the reason behind a state $\ensuremath{\rho}$ having a higher amount of entanglement (as quantified by the entanglement of formation) than a state ${\ensuremath{\rho}}^{\ensuremath{'}},$ but producing the same amount of Bell violation, is due to the fact that the amount of mixedness (as quantified by the linearized entropy) in $\ensuremath{\rho}$ is higher than that in ${\ensuremath{\rho}}^{\ensuremath{'}}.$ We counter their argument with examples. We extend these considerations to the von Neumann entropy. Our results suggest that the reason as to why equal amount of Bell violation requires different amounts of entanglement cannot, at least, be explained by mixedness alone.