QUANTUM COPYING - FUNDAMENTAL INEQUALITIES

How well can one copy an arbitrary qubit? To answer this question we c onsider two arbitrary vectors in a two-dimensional state space and an abstract copying transformation which will copy these two vectors. If the vectors are orthogonal, then perfect copies can be made. If they a re not, then errors will be introduced. The size of the error depends on the inner product of the two original vectors. We derive a lower bo und for the amount of noise induced by quantum copying. We examine bot h copying transformations which produce one copy and transformations w hich produce many, and show that the quality of each copy decreases as the number of copies increases.