Counterexamples to additivity of minimum output p-rényi entropy for p close to 0

Toby Cubitt, Aram W. Harrow, Debbie Leung, Ashley Montanaro, Andreas Winter

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Complementing recent progress on the additivity conjecture of quantum information theory, showing that the minimum output p-Rényi entropies of channels are not generally additive for p > 1, we demonstrate here by a careful random selection argument that also at p = 0, and consequently for sufficiently small p, there exist counterexamples. An explicit construction of two channels from 4 to 3 dimensions is given, which have non-multiplicative minimum output rank; for this pair of channels, numerics strongly suggest that the p-Rényi entropy is non-additive for all p ≃ 0.11. We conjecture however that violations of additivity exist for all p < 1.

Original languageEnglish
Pages (from-to)281-290
Number of pages10
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - Nov 2008
Externally publishedYes


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