Quantum Darwinism
Why do we agree on what's "out there"? Zurek's answer: a system S broadcasts its preferred-basis information into many environment fragments, so independent observers all read the same classical record. The plateau in mutual information vs fragment size is the moment a quantum fact becomes an objective one.
System + Environment
S ↔ E₁ ⊗ E₂ ⊗ … ⊗ Eₙ — system imprints redundantly on environment qubits
Mutual information I(S:F) vs fragment size
I(S:Fₓ) = H(S) + H(F) − H(S,F) — the plateau is where redundancy lives
why this is the key to objective reality
Pick a system S and let it interact with many environment qubits, each coupling at strength κ. After the interaction, look at any fragment F of the environment and ask: how much do I know about S from F alone? The answer is the mutual information I(S:F).
The shape of the curve is the punchline. For small F, you learn proportionally — each new qubit adds information. Then you hit the plateau: knowing about S is "redundantly encoded" in the environment, so additional fragments add nothing. Only at fragments near full size do you finally see quantum correlations that beat the classical limit.
R_δ = the fragment size needed to learn S to fidelity (1−δ). Small R_δ means information is broadcast redundantly across many fragments — the basis of classicality. This is what makes a quantum measurement look objective: different observers reading different fragments all end up agreeing on the same outcome.