In this work, we study asymmetric
(1→2) quantum cloning for pure states belonging to orbits generated by the orthogonal group. For every dimension
(d≥3), we determine the full region of achievable pairs of average single-copy fidelities. Using orthogonal covariance and the Brauer algebra, we reduce the optimization over all CPTP maps to a finite-dimensional spectral problem and construct explicit optimal cloning channels. We then apply the general results to four-mode fermionic states in the even-parity sector. Using triality, we identify the fixed-concurrence fermionic families with the orthogonal orbits considered in the first part of the paper. In particular, for pure Gaussian states we show that the symmetric locally optimal cloner is unique. We also compare local and global cloning and find that the channel optimal for the joint two-copy fidelity is different from the one optimal for the single-copy fidelities. Finally, we show that the locally optimal cloner cannot be implemented using only operations which preserve fermionic Gaussian states.
An optimal universal cloning transformation is derived that produces M copies of an unknown qubit from a pair of orthogonal qubits. For
M>6, the corresponding cloning fidelity is higher than that of the optimal copying of a pair of identical qubits. It is shown that this cloning transformation can be implemented probabilistically via parametric down conversion by feeding the signal and idler modes of a nonlinear crystal with orthogonally polarized photons.