Impossibility of deleting an unknown quantum state
A photon in an arbitrary polarization state cannot be cloned perfectly. But suppose that at our disposal we have several copies of a photon in an unknown state. Is it possible to delete the information content of one or more of these photons by a physical process? Specifically, if two photons are in the same initial polarization state, is there a mechanism that produces one photon in the same initial state and the other in some standard polarization state? If this could be done, then one would create a standard blank state onto which one could copy an unknown state approximately, by deterministic cloning or exactly, by probabilistic cloning. This could in principle be useful in quantum computation, where one could store new information in an already computed state by deleting the old information. Here we show, however, that the linearity of quantum theory does not allow us to delete a copy of an arbitrary quantum state perfectly. Though in a classical computer information can be deleted (reversibly) against a copy, the analogous task cannot be accomplished, even irreversibly, with quantum information.