Physics – Quantum Physics
Scientific paper
2007-07-07
Physical Review A 75 (2007) no. 6, P. 060304
Physics
Quantum Physics
3 pages
Scientific paper
10.1103/PhysRevA.75.060304
Given a quantum channel $\Phi $ in a Hilbert space $H$ put $\hat H_{\Phi}(\rho)=\min \limits_{\rho_{av}=\rho}\Sigma_{j=1}^{k}\pi_{j}S(\Phi (\rho_{j}))$, 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 $\hat H_{\Phi \otimes \Psi}(\rho)\ge \hat H_{\Phi}(Tr_{K}(\rho))+\hat H_{\Psi}(Tr_{H}(\rho))$ 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.
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