Radon transform in finite Hilbert space
Department of Physics, Technion, Israel Institute of Technology - Haifa 32000, Israel
Accepted: 29 February 2012
A novel analysis of finite-dimensional Hilbert space is outlined. The approach bypasses the general, inherent, difficulties present in handling angular variables in finite-dimensional problems: the finite-dimensional, d, odd prime, Hilbert space operators are underpinned with a finite geometry which provides intuitive perspectives to the physical operators. The analysis emphasizes a central role for projectors of mutual unbiased bases (MUB) states, extending thereby their use in finite-dimensional quantum-mechanics studies. Interrelations among the Hilbert space operators revealed via their (finite) dual affine plane geometry (DAPG) underpinning are displayed and utilized in formulating the finite-dimensional ubiquitous Radon transformation and its inverse illustrating phase-space-like physics encoded in lines and points of the geometry. The finite geometry required for our study is outlined.
PACS: 03.65.Ta – Foundations of quantum mechanics; measurement theory / 03.65.Wj – State reconstruction, quantum tomography / 02.10.Ox – Combinatorics; graph theory
© EPLA, 2012