Apostolos Vourdas (University of Bradford, UK)

Quantum systems with finite Hilbert space

Abstract:
   A finite quantum system with variables in Z(d) is considered. Phase space methods in this context (Heisenberg-Weyl group, Wigner and Weyl functions, etc) are discussed. A factorization of this system in terms of smaller subsystems is studied. Analytic representations in terms of Theta functions on a torus are discussed. The symplectic group Sp(2,Z(d)) is used for tomography in this context. The question of what happens at the `edge' (large d limit) is also addressed.