Symplectic transformations and quantum tomography in finite quantum systems

Abstract

Quantum systems where the position and momentum are in the ring (d is an odd integer) are considered. Symplectic transformations are studied, and the order of is calculated. Quantum tomography is also discussed. It is shown that measurements (used in the inverse Radon transform) need to be made on J2(d) lines (where J2(d) is the Jordan totient function).