QUANTUM TOMOGRAPHY, TELEPORTATION, AND CLONING

In this paper, in a simple unifying matrix framework, I will present general classification of all possible tomography methods, teleportation schemes, and optimal quantum cloning maps. We will see how every tomographic method or teleportation scheme corresponds to a choice of operator spanning sets, and how this framework also leads to methods for engineering new Bell measurements. On the other hand, the classification of all possible covariant cloning maps (that are optimal for a given criterion) includes all known types of cloning, and leads to methods for engineering new cloning machines, which can be physically realized through unitary transformation with ancilla, and/or via probabilistic quantum operations. Fidelity criteria for POVM’s can be exploited to achieve joint POVM’s via cloning. I will give concrete physical realizations in the paper.