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The Saturation of Several Universal Inequalities in Information-Processing
Lin Zhang, Junde Wu and Shao-Ming Fei
Strong subadditivity inequality of quantum entropy, proved by Lieb and Ruskai, is a powerful tool in quantum information theory. The fact that the strong subadditivity inequality saturated only by so-called Markov states is obtained in the recent literature [P. Hayden et al., Commun. Math. Phys. 246, 359 (2004).].
In this paper, we give a characterization of another equivalent version for strong subadditivity inequality. We discuss the coherent information saturating its upper bound as well. A necessary and sufficient condition for this saturation is derived. The possible applications are discussed.