Symplectic transformations and quantum tomography in finite quantum systems

摘要

Quantum systems where the position and momentum are in the ring Z(d) (d is an odd integer) are considered. Symplectic transformations are studied, and the order of Sp(2, Z(d)) is calculated. Quantum tomography is also discussed. It is shown that measurements (used in the inverse Radon transform) need to be made on J(2)(d) lines (where J(2)(d) is the Jordan totient function).