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We derive a strengthened monotonicity inequality for quantum relative entropy by employing properties of $\alpha$-R\'{e}nyi relative entropy.
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Ruskai, M.B.: Remarks on on Kim’s strong subadditivity matrix inequality: extensions and equality conditions. J. Math. Phys. 54
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Seshadreesan, K.P. , Berta, M., Wilde, M.M.: Rényi squashed entanglement, discord, and relative entropy differences. J. Phys. A: Math. Theor. 48
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