Using higher dimension (d>2) quantum systems, or qudits, indeed provides an advantage through greater control of the Hilbert space. In quantum key distribution (QKD) for example, qudits can enhance the average raw key rates as one can encode more bits per symbol. Even more, they improve the robustness or the noise tolerance of the QKD protocol -- Alice and Bob can distill a secret key in (noisier) conditions where using only qubits would have failed.
Using qutrits, one can address fundamental problems such as the Byzantine Agreement, enhance the efficiency of Toffoli gates, boost the classical channel capacity of a quantum channel (i.e. demonstrate the idea of superadditivity), etc.
I am not sure if I correctly understand the part about the 'advantage from the point of experimental realization', but what may be stated is that producing qudits is almost invariably more difficult than qubits. Therefore, cases where one may obtain an advantage because the experimental setup is easier to build or is somehow naturally more suited to producing and manipulating qudits than qubits are rather rare. In that sense, the total cost of a qutrit-based implementation & operation may not always surpass that of its lower-dimensional version (i.e. with qubits).
This post imported from StackExchange Physics at 2014-06-11 15:03 (UCT), posted by SE-user jayann