Ensemble-steering attack on quantum bit commitment

If the two honest quantum state ensembles have the same density operator, their independently prepared blocks are perfectly hiding. A dishonest sender can instead send one half of a purification of a density operator and retain the other. The Hughston–Jozsa–Wootters theorem allows a measurement of the retained system to prepare either honest ensemble after commitment. If verification checks only the declared states, either opening is then accepted with the honest probabilities. This gives a concrete failure of binding while preserving perfect hiding.