Some problems of quantum information, cloning, estimation and testing of states, universal coding etc., are special example of the following `state convertibility' problem. In this paper, we consider the dual of this problem, 'observable conversion problem'. Given families of operators $\{ L_\theta}\}_{ \theta\in\Theta}$ and $\{ M_\theta}\}_{ \theta\in\Theta}$ , we ask whether there is a completely positive (sub) unital map which sends $\{ L_\theta}\}$ to $\{ M_\theta}\}$ for each { \theta}. We give necessary and sufficient conditions for the convertibility in some special cases.
Categories: quant-ph