Quantum No-Cloning Theorem (2D)

The no-cloning theorem is one of the load-bearing walls of quantum information theory: no process, however clever, can turn one copy of an unknown quantum state into two identical copies. This 2D companion projects the Bloch sphere onto a draggable disk and lets you attack a hidden qubit state two ways — a naive "measure it in some basis and resend the result" intercept, and the mathematically optimal universal quantum cloning machine — driven by the exact same closed-form fidelity model as the 3D version. Run trials to watch the intercept strategy's fidelity scatter and converge to its hard 2/3 ceiling, or switch to the optimal cloner to see the best achievable 5/6 fidelity realised as a shrunken Bloch vector — a mixed state, because a perfect clone is exactly what quantum mechanics forbids.