Finite quantum systems are considered and dual quantities are defined with a finite Fourier transform. Ladder operators that translate the eigenstates of these quantities are shown to form a finite Weyl group. Dual measurements are introduced and shown to obey certain entropic inequalities. A factorization of these systems into subsystems with the use of number-theoretic results is also presented.

• Received 21 September 1992

DOI:https://doi.org/10.1103/PhysRevA.47.3523