ASYMMETRIC QUANTUM CLONING MACHINES

A family of asymmetric cloning machines for quantum bits and N-dimensi onal quantum states is introduced. These machines produce two approxim ate copies of a single quantum state that emerge from two distinct cha nnels. In particular, an asymmetric Pauli cloning machine is defined.t hat makes two imperfect copies of a quantum bit, while the overall inp ut-to-output operation for each copy is a Pauli channel. A no-cloning inequality is derived, characterizing the impossibility of copying imp osed by quantum mechanics. If p and p' are the probabilities of the de polarizing channels associated with the two outputs, the domain in (ro ot p, root p')-space located inside a particular ellipse representing close-to-perfect cloning is forbidden. This ellipse tends to a circle when copying an N-dimensional state with N --> infinity, which has a s imple semi-classical interpretation. The symmetric Pauli cloning machi nes are then used to provide an upper bound on the quantum capacity of the Pauli channel of probabilities p(x), p(y) and p(z). The capacity is proven to be vanishing if (root p(x), root p(y), root p(z)) lies ou tside an ellipsoid whose pole coincides with the depolarizing channel that underlies the universal cloning machine.:Finally, the tradeoff be tween the quality of the two copies is shown to result from.a compleme ntarity akin to Heisenberg uncertainty principle.