The majorization criterion: Given a bipartite state, it is entangled if Eq. (\[dibakar\]) is violated. However, it was shown in Ref. [@Hiroshima], that a state that is not detected by the positive partial transposition criterion, will not be detected by the majorization criterion either. Nevertheless, the criterion has other important implications. We will now discuss one such.

Let us reiterate an interesting fact about the singlet state: The global state is pure, while the local states are completely mixed. In particular, this implies that the von Neumann entropy [^2] of the singlet is lower than the von Neumann entropies of either of the local states. Since the von Neumann entropy can be used to quantify disorder in a given state, there exist global states whose disorder is lower than the any of the local states. This is a nonclassical fact as for two classical random variables, the Shannon entropy [^3] of the joint distribution cannot be smaller than that of either. In Ref. [@horo_ent_sep], it was shown that a similar fact is true for separable states:\
**Theorem 5**\
*If a state $\rho_{AB}$ is separable, $$\label{chandrima}
S (\rho_{AB}) \geq S (\rho_A ), \quad  and \quad S (\rho_{AB}) \geq S (\rho_B ).$$* 