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arXiv · 0707.1097

The strong superadditivity conjecture holds for the quantum depolarizing channel in any dimension

Grigori G. Amosov
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Abstract

Given a quantum channel $Φ$ in a Hilbert space $H$ put $\hat H_Φ(ρ)=\min \limits_{ρ_{av}=ρ}Σ_{j=1}^{k}π_{j}S(Φ(ρ_{j}))$, where $ρ_{av}=Σ_{j=1}^{k}π_{j}ρ_{j}$, the minimum is taken over all probability distributions $π=\{π_{j}\}$ and states $ρ_{j}$ in $H$, $S(ρ)=-Trρ\logρ$ is the von Neumann entropy of a state $ρ$. The strong superadditivity conjecture states that $\hat H_{Φ\otimes Ψ}(ρ)\ge \hat H_Φ(Tr_{K}(ρ))+\hat H_Ψ(Tr_{H}(ρ))$ for two channels $Φ$ and $Ψ$ in Hilbert spaces $H$ and $K$, respectively. We have proved the strong superadditivity conjecture for the quantum depolarizing channel in any dimensions.

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Grigori G. Amosov. 2007-07-07. The strong superadditivity conjecture holds for the quantum depolarizing channel in any dimension. https://doi.org/10.1103/physreva.75.060304

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