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Relating zero discord to the strong subadditivity of the Von Neumann entropy, Datta proved that a state has zero $\\mathit{cq}$ discord iff and only if it can be written in the form $\\sum_i p_i\\, |i\\rangle\\langle i|\\otimes \\rho^B_i$ for $p_i$ a probability distribution, $|i\\rangle$ a basis of the $A$ system and $\\rho^B_i$ states of the $B$ system. 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