  Operator-Schmidt decompositions of the quantum Fourier transform on C^N1
tensor C^N2 are computed for all N1, N2 > 1. The decomposition is shown to be
completely degenerate when N1 is a factor of N2 and when N1>N2. The first known
special case, N1=N2=2^n, was computed by Nielsen in his study of the
communication cost of computing the quantum Fourier transform of a collection
of qubits equally distributed between two parties. [M. A. Nielsen, PhD Thesis,
University of New Mexico (1998), Chapter 6, arXiv:quant-ph/0011036.] More
generally, the special case N1=2^n1<2^n2=N2 was computed by Nielsen et. al. in
their study of strength measures of quantum operations. [M.A. Nielsen et. al,
(accepted for publication in Phys Rev A); arXiv:quant-ph/0208077.] Given the
Schmidt decompositions presented here, it follows that in all cases the
communication cost of exact computation of the quantum Fourier transform is
maximal.
