Process-optimized phase-covariant quantum cloning

After the appearance of no-cloning theorem, approximate quantum cloning machines (QCMs) has become a well-studied subject in information theory. Among several measures to quantify performance QCM, single-qudit fidelity and global have been most widely used. In this paper we compute optimal for phase-covariant via semidefinite programming optimization, thereby completing remaining gap previous results on QCMs. We also consider simulations transpose map, both by direct optimization composition component-wise For map method is suboptimal whereas asymptotically optimal.