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

References in corpus (2)

• Entanglement enhanced classical capacity of quantum communication channels with correlated noise in arbitrary dimensions
• On Weyl channels being covariant with respect to the maximum commutative group of unitaries

Cited by in corpus (1)

• Some Open Problems in Quantum Information Theory