No-cloning theorem for a single observable

The concept of observable cloning introduced by Ferraro et al. [J. Phys. A: Math. Theor. 39, L219, 2006] is developed in some essential aspects. As figure of merit, we justify a relative entropy of the joint distribution at the output to the product of independent distributions at the input. It is shown that the impossibility of observable cloning can be caused by set of possible input states. Like incompatibility of observables, this fact is also key aspect in the cloning process for class of observables. A no-cloning principle for a single observable is formulated. For a given observable, there exist pairs of states such that perfect cloning is impossible. We discuss some properties of those sets that do not allow the perfect cloning of the prescribed observable. PACS: 03.67.-a, 03.65.Ta