Quantum Darwinism: Redundancy Spectrum (2D)

This 2D companion to the 3D pointer-state simulator visualizes quantum Darwinism through its central measurable quantity — the redundancy spectrum — instead of a rotating shell of environment fragments. A qubit prepared away from its pointer basis is coupled to a register of environment fragments; as interaction time advances, the qubit's pointer-basis populations stay fixed while coherence between them collapses, and each fragment's own record fidelity grows toward 1. Rather than approximating how many fragments an observer would need to sample to learn the outcome, this version computes it exactly: a dynamic-programming convolution over every fragment's individual fidelity, sampled best-first, yields the true probability that a majority vote over any number of fragments recovers the hidden outcome. Watch how quickly that curve saturates near 99% confidence with only a small fraction of the environment — the plateau that makes a classical, objective outcome available to many independent observers at once.