Quantum coding with systems with finite Hilbert space

Angle states and operators are defined in a (2j + 1)-dimensional angular momentum Hilbert space H through Fourier transform. Displacement operators in the corresponding quantum phase space which in this case is a toroidal lattice, are generators of SU(2j + 1) transformations in H. In this context, a concatenated code is studied. In the first step the code is the space H-A spanned by the direct products of N angular momentum states with the same m. In the second step the code is the space H-B spanned by the direct products of M angle states of the space H-A, with the same m.