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

Abstract

Given a quantum channel $\Phi$ in a Hilbert space $H$ put ${\hat{H}}_{\Phi }(\rho )=\underset{{\rho }_{av}=\rho }{\min }{\Sigma }_{j=1}^k{\pi }_{j}S(\Phi ({\rho }_j))$, where ${\rho }_{av}={\Sigma }_{j=1}^k{\pi }_j{\rho }_j$, the minimum is taken over all probability distributions $\pi =\{{\pi }_j\}$ and states ${\rho }_j$ in $H$, $S(\rho )=-Tr\rho \log \rho$ is the von Neumann entropy of a state $\rho$. The strong superadditivity conjecture states that ${\hat{H}}_{\Phi \otimes \Psi }(\rho )\ge {\hat{H}}_{\Phi }(T{r}_K(\rho ))+{\hat{H}}_{\Psi }(T{r}_H(\rho ))$ for two channels $\Phi$ and $\Psi$ in Hilbert spaces $H$ and $K$, respectively. We have proved the strong superadditivity conjecture for the quantum depolarizing channel in any dimensions.

3 pages

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• Additivity of entanglement of formation via entanglement-breaking space
• Generalizations of $2$-dimensional diagonal quantum channels with constant Frobenius norm
• How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation
• Superclassical non-Markovian open quantum dynamics
• Pilot Quantum Error Correction for Global-Scale Quantum Communications
• Superoperator master equations for depolarizing dynamics
• On estimating the output entropy of a tensor product of the quantum phase-damping channel with an arbitrary channel