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Non-Additivity of Minimum Output p-$\mathbf{R\acute{e}nyi}$ Entropy

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Preprint
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arXiv
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Abstract

Hastings disproved additivity conjecture for minimum output entropy by using random unitary channels. In this note, we employ his approach to show that minimum output $p-$R\'{e}nyi entropy is non-additive for $p\in(0,p_0)\cup(1-p_0,1)$ where $p_0\approx 0.2855$.

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