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

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arxiv 1006.1733 v2 pith:Q63JCVZS submitted 2010-06-09 quant-ph

Nengkun Yu , Mingsheng Ying This is my paper · ORCID
classification quant-ph
keywords entropyminimumoutputacuteadditivityapproachapproxchannels
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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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  1. Counterexamples to additivity of minimum output $p$-R\'enyi entropy of quantum channels for $p>3/4$ and $0\leq p<1/4$

    quant-ph 2026-07 accept novelty 7.0 of 10

    For every Rényi order p<1/4 or p>3/4, some finite-dimensional quantum channels have non-additive minimum output p-Rényi entropy.

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