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Arguably the deepest fact known about the von~Neumann entropy, the strong subadditivity inequality is a potent hammer in the quantum information theorist's toolkit. This short tutorial describes a simple proof of strong subadditivity due to Petz [Rep. on Math. Phys. 23 (1), 57--65 (1986)]. It assumes only knowledge of elementary linear algebra and quantum mechanics.
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Nielsen et al. (2005) studied this question.
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