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"How much information about a system $\mathcal{S}$ can one extract from afragment $\mathcal{F}$ of the environment $\mathcal{E}$ that decohered it?" isthe central question of Quantum Darwinism. To date, most answers relied on thequantum mutual information of $\mathcal{SF}$, or on the Holevo bound on thechannel capacity of $\mathcal{F}$ to communicate the classical informationencoded in $\mathcal{S}$. These are reasonable upper bounds on what is reallyneeded but much harder to calculate -- the accessible information in thefragment $\mathcal{F}$ about $\mathcal{S}$. We consider a model based onimperfect c-not gates where all the above can be computed, and discuss itsimplications for the emergence of objective classical reality. We find that allrelevant quantities, such as the quantum mutual information as well as variousbounds on the accessible information exhibit similar behavior. In the regimerelevant for the emergence of objective classical reality this includes scalingindependent of the quality of the imperfect c-not gates or the size of$\mathcal{E}$, and even nearly independent of the initial state of$\mathcal{S}$.

Eavesdropping on the Decohering Environment: Quantum Darwinism, Amplification, and the Origin of Objective Classical Reality