On Conjectures of Classical and Quantum Correlations in Bipartite States

Professor S. Luo in [Phys. Rev. A 82, 052122(2010)] proposed two conjectures on the classical correlation and quantum correlation in a bipartite state ρAB, respectively. In this paper, we prove the conjecture on the classical correlation completely. Moreover, we show that Q(ρAB) 6 S(ρB) is always valid, and the conjecture on quantum correlation is true if S(ρB) 6 S(ρA) or ρAB is separable. We obtain also a class of states ρAB satisfies that S(ρA) 6 S(ρB), but Q(ρAB) 6 S(ρA), so the conjecture on quantum correlation is also true for them.