  Attempts at cloning a quantum system result in the introduction of
imperfections in the state of the copies. This is a consequence of the
no-cloning theorem, which is a fundamental law of quantum physics and the
backbone of security for quantum communications. Although such perfect copies
are prohibited, a quantum state may be copied with maximal accuracy via various
optimal cloning schemes. Optimal quantum cloning, which lies at the border of
the physical limit imposed by the no-signalling theorem and the Heisenberg
uncertainty principle, has been experimentally realized for low dimensional
photonic states. However, an increase in the dimensionality of quantum systems
is greatly beneficial to quantum computation and communication protocols.
Nonetheless, no experimental demonstration of optimal cloning machines has
hitherto been shown for high-dimensional quantum systems. Here, we perform
optimal cloning of high-dimensional photonic states by means of the
symmetrization method. We show the universality of our technique by conducting
cloning of numerous arbitrary input states, and fully characterize our cloning
machine by performing quantum state tomography on \emph{cloned} photons. In
addition, a cloning attack on a Bennett and Brassard (BB84) quantum key
distribution protocol is experimentally demonstrated in order to reveal the
robustness of high-dimensional states in quantum cryptography.

Quantum Physics