Quantum marginal inequalities and the conjectured entropic inequalities

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A conjecture -- the modified super-additivity inequality of relative entropy -- was proposed in Zhang2012: There exist three unitary operators Uₐ∈ ₐ,UB∈, and UAB∈ ₐ such that (UABρABU†AB||σAB) (UₐρₐU†ₐ||σₐ) + (UBρBU†B||σB), where the reference state σ is required to be full-ranked. A numerical study on the conjectured inequality is conducted in this note. The results obtained indicate that the modified super-additivity inequality of relative entropy seems to hold for all qubit pairs.