Fig. 2. Optimal cloning fidelity for various dimensions.

(A) Experimental values of the cloning fidelities are shown for each d number of elements of the logical basis, along with theoretical values, for various dimensions d. (B) The average cloning fidelities (blue dots) are plotted for various dimensions, along with probability matrices $\mathcal{P}(|\mathit{i}\rangle ,|\mathrm{\psi }\rangle )$ of detecting a cloned photon in any output state |i〉 of the OAM logical basis, given an input state |ψ〉 of the same basis. The diagonal elements of the probability matrices correspond to the cloning fidelity of each element of the basis. The light and dark gray shaded areas correspond to fidelities not accessible by state estimation and 1 → 2 optimal symmetric UQCM, respectively. In quantum cryptography, a more effective class of quantum hacking, namely, coherent attacks (1), yields larger fidelities illustrated by the dim gray shaded area.