A general scheme for ensemble purification

We exhibit a general procedure to purify any given ensemble by identifying an appropriate interaction between the physical system S of the ensemble and the reference system K. We show that the interaction can be chosen in such a way to lead to a spatial separation of the pair S–K. As a consequence, one can use it to prepare at a distance different equivalent ensembles. The argument associates a physically precise procedure to the purely formal and fictitious process usually considered in the literature. We conclude with an illuminating example taken from quantum computational theory.