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

TL;DR

This paper proves that the strong superadditivity conjecture holds for the quantum depolarizing channel across all dimensions, confirming a key property of this important quantum channel.

Contribution

The paper establishes the validity of the strong superadditivity conjecture specifically for the quantum depolarizing channel in any dimension, a significant theoretical advancement.

Findings

Proves strong superadditivity for quantum depolarizing channels in all dimensions

Confirms the conjecture's applicability to a widely used quantum channel

Enhances understanding of entropy properties in quantum information theory

Abstract

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.