Quantum No-Cloning Theorem

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 simulator lets you set a hidden qubit state on the Bloch sphere and attack it two ways — a naive "measure it in some basis and resend the result" intercept, and the mathematically optimal universal quantum cloning machine. 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.