The state, say | psi > = p^0.5 | 00 > + (1-p)^0.5 | 11 > has entanglement of formation equal to 0.5 ebits at p = 0.11. Similarly the state, say rho = (1-f)/3 I + (4f - 1)/3 | psi^- > < psi^- |, where | psi^- > is the maximally entangled state, has the entanglement of formation 0.5 ebits at f = 0.813. But there are certain tasks where the later state is not useful but the earlier state is. So what is the reason behind this kind of asymmetry?
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