Optimal real state cloning inddimensions

We present an explicit transformation of optimal asymmetric $1\ensuremath{\rightarrow}2$ real state cloning in two dimensions. Interestingly, the distribution of the two fidelities of the cloning is the same as its counterpart in optimal asymmetric phase-covariant cloning. We also generalize the cloner to the $d$-dimensional case and derive the explicit transformation of the optimal symmetric $1\ensuremath{\rightarrow}2$ real state cloning in the $d$-dimensional system. The maximal fidelity of two clones obtained coincides with the theoretical value [P. Vavez and N. J. Cerf, Phys. Rev. A 68, 032313 (2003)].