Quantum broadcasting, copying, and deleting

Abstract

Even with a good set of tools for maintaining the coherence properties of quantum states, there exist fundamental limitations on the set of tasks that can be carried out in quantum communication and quantum information processing. In this brief chapter, we consider some of these limitations and methods of working within them to approximate quantum tasks that are desired but cannot be performed perfectly. For example, perfect quantum deleting cannot be performed due to the linearity of quantum mechanics. Similarly, the no-cloning theorem discussed in Section 9.5, which is also based on the superposition principle, precludes the exact copying of an unknown quantuminformation bearing pure state. Particularly important for quantum communication are limitations arising in the context of state broadcasting, that is, the distribution of the same quantum information to a number of parties.