Functional Information in Quantum Darwinism: An Operational Measure of Objectivity

Abstract

Quantum Darwinism explains the emergence of classical objectivity through the redundant encoding of pointer information in environmental fragments. However, existing diagnostics rely on arbitrary thresholds or structural assumptions that limit their operational applicability. We develop a framework based on \emph{functional information}, $\FI(\delta) = \log_2 R_\delta$, which quantifies objectivity as the abundance of environment fragments that individually carry at least $(1-\delta)H_S$ bits of classically accessible pointer information, as bounded by the Holevo quantity. Using onset statistics rather than parametric fits, we extract redundancy $R_\delta$ from the fragment size at which adequacy becomes typical. Simulations of a heterogeneous pure-dephasing model reveal three robust features: rapid early-time growth of $\ln R_\delta$, smooth crossover to saturation, and capacity-limited plateaus at $\FI^{\mathrm{plateau}} \lesssim \log_2 N$. We establish thermodynamic constraints showing that each additional bit of $\FI$ doubles the minimal heat dissipation required for record stabilization. These results frame classical objectivity as a quantifiable, resource-limited phenomenon.