The 1/e Information Horizon as a Universal Quantum-Classical Boundary: A No-Go Theorem for Passive Dynamics

We establish fundamental constraints on quantum information accessibility at the boundary between quantum and classical descriptions of physical systems. Through information-theoretic analysis of bipartite entanglement structure, we prove that the Schmidt concentration value Kc =1/e ≈ 0. 368 represents a universal critical manifold—the unique configuration that simultaneously maximizes both quantum correlations and classical information extraction efficiency. This “information horizon” emerges naturally from the optimization of von Neumann entropy subject to measurement constraints, coinciding with the entanglement structure observed in biological quantum systems such as the Fenna-Matthews-Olson photosynthetic complex. We derive a no-go theorem: any passive measurement protocol (fixed measurement rate) drives quantum circuits either toward volume-law chaos (Kc → 0) or Zeno frozen localization (Kc → 1), making the 1/e horizon inaccessible without active control. In contrast, adaptive feedback protocols successfully stabilize systems at criticality, achieving ⟨Kc⟩ = 0. 353 ± 0. 017 across system sizes N ∈ 12, 14, 16 qubits. The observed finite size oscillations are characteristic of control stabilized critical points, with ensemble mean consistent with 1/e within statistical error. Numerical validation via exact diagonalization up to 16 qubits confirms the theoretical predictions, with feedback control achieving steady-state values within 5% of target across multiple system sizes despite critical finite size oscillations. These results suggest that biological quantum systems do not require fine-tuned parameters to maintain criticality, but rather simple feedback architectures—providing a selection-pressure-free evolutionary pathway to quantum-enhanced functionality.