Entanglement Purification — Cascade & Ensemble (2D)

This is the 2D statistical counterpart to the 3D BBPSSW purification scene: instead of watching one pair of stations trade qubits in 3D space, it draws the protocol as what it actually is mathematically — a binary recursion with a per-round success probability. The top panel renders a single distillation attempt as a literal merge-tree dendrogram, with a CNOT-plus-measurement gate glyph flashing at every node where two noisy pairs are combined into one cleaner (or discarded) pair. The bottom panel runs a genuinely independent Monte-Carlo simulation — hundreds of separate chains stepping through the identical recursion — and plots the empirical surviving fraction against the exact theoretical curve ∏ p_succ(Fᵢ), so you can watch the law of large numbers pull the bars onto the dashed prediction as the ensemble size grows. Tune the raw fidelity and purification depth to see the classic fidelity-versus-yield trade-off from two angles at once: one tree's fate, and the population statistics behind it.